﻿ Generalized Stirling_2 Triangles
 Generalized Stirling_2 Triangle k = -6 Sum: A049412 all partitions: A134278 ~ by length: A049385 ~ by biggest part: A157396 diagonal: A008548 1 [1] [1] [1] 1 1 [1] [1] [1] 1 7 [1,6] [6,1] [1,6] 6 85 [1,18,66] [66,18,1] [1,18,66] 66 1465 [1,36,108,264,1056] [1056,372,36,1] [1,144,264,1056] 1056 32677 [1,60,540,660,3960,5280,22176] [22176,9240,1200,60,1] [1,600,4620,5280,22176] 22176 Generalized Stirling_2 Triangle k = -5 Sum: A049120 all partitions: A134273 ~ by length: A049029 ~ by biggest part: A157397 diagonal: A007696 1 [1] [1] [1] 1 1 [1] [1] [1] 1 6 [1,5] [5,1] [1,5] 5 61 [1,15,45] [45,15,1] [1,15,45] 45 871 [1,30,75,180,585] [585,255,30,1] [1,105,180,585] 585 15996 [1,50,375,450,2250,2925,9945] [9945,5175,825,50,1] [1,425,2700,2925,9945] 9945 Generalized Stirling_2 Triangle k = -4 Sum: A049119 all partitions: A134149 ~ by length: A035469 ~ by biggest part: A157398 diagonal: A007559 1 [1] [1] [1] 1 1 [1] [1] [1] 1 5 [1,4] [4,1] [1,4] 4 41 [1,12,28] [28,12,1] [1,12,28] 28 465 [1,24,48,112,280] [280,160,24,1] [1,72,112,280] 280 6721 [1,40,240,280,1120,1400,3640] [3640,2520,520,40,1] [1,280,1400,1400,3640] 3640 Generalized Stirling_2 Triangle k = -3 Sum: A049118 all partitions: A134144 ~ by length: A035342 ~ by biggest part: A157399 diagonal: A001147 1 [1] [1] [1] 1 1 [1] [1] [1] 1 4 [1,3] [3,1] [1,3] 3 25 [1,9,15] [15,9,1] [1,9,15] 15 211 [1,18,27,60,105] [105,87,18,1] [1,45,60,105] 105 2236 [1,30,135,150,450,525,945] [945,975,285,30,1] [1,165,600,525,945] 945 Generalized Stirling_2 Triangle k = -2 Sum: A000262 all partitions: A130561 ~ by length: A105278 ~ by biggest part: A157400 diagonal: A000142 1 [1] [1] [1] 1 1 [1] [1] [1] 1 3 [1,2] [2,1] [1,2] 2 13 [1,6,6] [6,6,1] [1,6,6] 6 73 [1,12,12,24,24] [24,36,12,1] [1,24,24,24] 24 501 [1,20,60,60,120,120,120] [120,240,120,20,1] [1,80,180,120,120] 120 Generalized Stirling_2 Triangle k = -1 Sum: A000110 all partitions: A036040 ~ by length: A008277 ~ by biggest part: A080510 diagonal: A000012 1 [1] [1] [1] 1 1 [1] [1] [1] 1 2 [1,1] [1,1] [1,1] 1 5 [1,3,1] [1,3,1] [1,3,1] 1 15 [1,6,3,4,1] [1,7,6,1] [1,9,4,1] 1 52 [1,10,15,10,10,5,1] [1,15,25,10,1] [1,25,20,5,1] 1 Generalized Stirling_2 Triangle k = 0 Sum: A000012 all partitions: A155972 ~ by length: A023531 ~ by biggest part: A000000 diagonal: A000000 1 [1] [1] [1] 1 1 [1] [1] [1] 1 1 [1,0] [0,1] [1,0] 0 1 [1,0,0] [0,0,1] [1,0,0] 0 1 [1,0,0,0,0] [0,0,0,1] [1,0,0,0] 0 1 [1,0,0,0,0,0,0] [0,0,0,0,1] [1,0,0,0,0] 0 Generalized Stirling_2 Triangle k = 1 Sum: A001515 all partitions: A143171 ~ by length: A001497 ~ by biggest part: A157401 diagonal: A001147 1 [1] [1] [1] 1 1 [1] [1] [1] 1 2 [1,1] [1,1] [1,1] 1 7 [1,3,3] [3,3,1] [1,3,3] 3 37 [1,6,3,12,15] [15,15,6,1] [1,9,12,15] 15 266 [1,10,15,30,30,75,105] [105,105,45,10,1] [1,25,60,75,105] 105 Generalized Stirling_2 Triangle k = 2 Sum: A015735 all partitions: A143172 ~ by length: A004747 ~ by biggest part: A157402 diagonal: A008544 1 [1] [1] [1] 1 1 [1] [1] [1] 1 3 [1,2] [2,1] [1,2] 2 17 [1,6,10] [10,6,1] [1,6,10] 10 145 [1,12,12,40,80] [80,52,12,1] [1,24,40,80] 80 1661 [1,20,60,100,200,400,880] [880,600,160,20,1] [1,80,300,400,880] 880 Generalized Stirling_2 Triangle k = 3 Sum: A016036 all partitions: A143173 ~ by length: A000369 ~ by biggest part: A157403 diagonal: A008545 1 [1] [1] [1] 1 1 [1] [1] [1] 1 4 [1,3] [3,1] [1,3] 3 31 [1,9,21] [21,9,1] [1,9,21] 21 361 [1,18,27,84,231] [231,111,18,1] [1,45,84,231] 231 5626 [1,30,135,210,630,1155,3465] [3465,1785,345,30,1] [1,165,840,1155,3465] 3465 Generalized Stirling_2 Triangle k = 4 Sum: A028575 all partitions: A144267 ~ by length: A011801 ~ by biggest part: A157404 diagonal: A008546 1 [1] [1] [1] 1 1 [1] [1] [1] 1 5 [1,4] [4,1] [1,4] 4 49 [1,12,36] [36,12,1] [1,12,36] 36 721 [1,24,48,144,504] [504,192,24,1] [1,72,144,504] 504 14177 [1,40,240,360,1440,2520,9576] [9576,3960,600,40,1] [1,280,1800,2520,9576] 9576 Generalized Stirling_2 Triangle k = 5 Sum: A028844 all partitions: A144268 ~ by length: A013988 ~ by biggest part: A157405 diagonal: A008543 1 [1] [1] [1] 1 1 [1] [1] [1] 1 6 [1,5] [5,1] [1,5] 5 71 [1,15,55] [55,15,1] [1,15,55] 55 1261 [1,30,75,220,935] [935,295,30,1] [1,105,220,935] 935 29906 [1,50,375,550,2750,4675,21505] [21505,7425,925,50,1] [1,425,3300,4675,21505] 21505

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