Generalized Stirling_1 Triangle k = -6 Sum: A049402 all partitions: A144356 ~ by length: A049374 ~ by biggest part: A157386 diagonal: A001725 1 [1] [1] [1] 1 1 [1] [1] [1] 1 7 [1,6] [6,1] [1,6] 6 61 [1,18,42] [42,18,1] [1,18,42] 42 649 [1,36,108,168,336] [336,276,36,1] [1,144,168,336] 336 8245 [1,60,540,420,2520,1680,3024] [3024,4200,960,60,1] [1,600,2940,1680,3024] 3024 Generalized Stirling_1 Triangle k = -5 Sum: A049378 all partitions: A144355 ~ by length: A049353 ~ by biggest part: A157385 diagonal: A001720 1 [1] [1] [1] 1 1 [1] [1] [1] 1 6 [1,5] [5,1] [1,5] 5 46 [1,15,30] [30,15,1] [1,15,30] 30 436 [1,30,75,120,210] [210,195,30,1] [1,105,120,210] 210 4956 [1,50,375,300,1500,1050,1680] [1680,2550,675,50,1] [1,425,1800,1050,1680] 1680 Generalized Stirling_1 Triangle k = -4 Sum: A049377 all partitions: A144354 ~ by length: A049352 ~ by biggest part: A157384 diagonal: A001715 1 [1] [1] [1] 1 1 [1] [1] [1] 1 5 [1,4] [4,1] [1,4] 4 33 [1,12,20] [20,12,1] [1,12,20] 20 273 [1,24,48,80,120] [120,128,24,1] [1,72,80,120] 120 2721 [1,40,240,200,800,600,840] [840,1400,440,40,1] [1,280,1000,600,840] 840 Generalized Stirling_1 Triangle k = -3 Sum: A049376 all partitions: A144353 ~ by length: A046089 ~ by biggest part: A157383 diagonal: A001710 1 [1] [1] [1] 1 1 [1] [1] [1] 1 4 [1,3] [3,1] [1,3] 3 22 [1,9,12] [12,9,1] [1,9,12] 12 154 [1,18,27,48,60] [60,75,18,1] [1,45,48,60] 60 1306 [1,30,135,120,360,300,360] [360,660,255,30,1] [1,165,480,300,360] 360 Generalized Stirling_1 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_1 Triangle k = -1 Sum: A000142 all partitions: A102189 ~ by length: A008275 ~ by biggest part: A126074 diagonal: A000142 1 [1] [1] [1] 1 1 [1] [1] [1] 1 2 [1,1] [1,1] [1,1] 1 6 [1,3,2] [2,3,1] [1,3,2] 2 24 [1,6,3,8,6] [6,11,6,1] [1,9,8,6] 6 120 [1,10,15,20,20,30,24] [24,50,35,10,1] [1,25,40,30,24] 24 Generalized Stirling_1 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_1 Triangle k = 1 Sum: A000085 all partitions: A144357 ~ by length: A049403 ~ by biggest part: A157391 diagonal: A130716 1 [1] [1] [1] 1 1 [1] [1] [1] 1 2 [1,1] [1,1] [1,1] 1 4 [1,3,0] [0,3,1] [1,3,0] 0 10 [1,6,3,0,0] [0,3,6,1] [1,9,0,0] 0 26 [1,10,15,0,0,0,0] [0,0,15,10,1] [1,25,0,0,0] 0 Generalized Stirling_1 Triangle k = 2 Sum: A049425 all partitions: A144358 ~ by length: A049404 ~ by biggest part: A157392 diagonal: A008279 1 [1] [1] [1] 1 1 [1] [1] [1] 1 3 [1,2] [2,1] [1,2] 2 9 [1,6,2] [2,6,1] [1,6,2] 2 33 [1,12,12,8,0] [0,20,12,1] [1,24,8,0] 0 141 [1,20,60,20,40,0,0] [0,40,80,20,1] [1,80,60,0,0] 0 Generalized Stirling_1 Triangle k = 3 Sum: A049426 all partitions: A144877 ~ by length: A049410 ~ by biggest part: A157393 diagonal: A008279 1 [1] [1] [1] 1 1 [1] [1] [1] 1 4 [1,3] [3,1] [1,3] 3 16 [1,9,6] [6,9,1] [1,9,6] 6 76 [1,18,27,24,6] [6,51,18,1] [1,45,24,6] 6 436 [1,30,135,60,180,30,0] [0,210,195,30,1] [1,165,240,30,0] 0 Generalized Stirling_1 Triangle k = 4 Sum: A049427 all partitions: A144878 ~ by length: A049424 ~ by biggest part: A157394 diagonal: A008279 1 [1] [1] [1] 1 1 [1] [1] [1] 1 5 [1,4] [4,1] [1,4] 4 25 [1, 12, 12] [12, 12, 1] [1, 12, 12] 12 145 [1,24,48,48,24] [24,96,24,1] [1,72,48,24] 24 1025 [1,40,240,120,480,120,24] [24,600,360,40,1] [1,280,600,120,24] 24 Generalized Stirling_1 Triangle k = 5 Sum: A049431 all partitions: A144879 ~ by length: A049411 ~ by biggest part: A157395 diagonal: A008279 1 [1] [1] [1] 1 1 [1] [1] [1] 1 6 [1,5] [5,1] [1,5] 5 36 [1,15,20] [20,15,1] [1,15,20] 20 246 [1,30,75,80,60] [60,155,30,1] [1,105,80,60] 60 2046 [1,50,375,200,1000,300,120] [120,1300,575,50,1] [1,425,1200,300,120] 120

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