﻿ Bessel-Triangles
 Bessel-Triangle k = -6 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 7 [1,6] [6,1] [1,6] 103 [1,18,84] [84,18,1] [1,18,84] 2497 [1,36,108,336,2016] [2016,444,36,1] [1,144,336,2016] 89137 [1,60,540,840,5040,10080,72576] [72576,15120,1380,60,1] [1,600,5880,10080,72576] Bessel-Triangle k = -5 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 6 [1,5] [5,1] [1,5] 76 [1,15,60] [60,15,1] [1,15,60] 1606 [1,30,75,240,1260] [1260,315,30,1] [1,105,240,1260] 50646 [1,50,375,600,3000,6300,40320] [40320,9300,975,50,1] [1,425,3600,6300,40320] Bessel-Triangle k = -4 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 5 [1,4] [4,1] [1,4] 53 [1,12,40] [40,12,1] [1,12,40] 953 [1,24,48,160,720] [720,208,24,1] [1,72,160,720] 26041 [1,40,240,400,1600,3600,20160] [20160,5200,640,40,1] [1,280,2000,3600,20160] Bessel-Triangle k = -3 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 4 [1,3] [3,1] [1,3] 34 [1,9,24] [24,9,1] [1,9,24] 502 [1,18,27,96,360] [360,123,18,1] [1,45,96,360] 11566 [1,30,135,240,720,1800,8640] [8640,2520,375,30,1] [1,165,960,1800,8640] Bessel-Triangle k = -2 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 3 [1,2] [2,1] [1,2] 19 [1,6,12] [12,6,1] [1,6,12] 217 [1,12,12,48,144] [144,60,12,1] [1,24,48,144] 4041 [1,20,60,120,240,720,2880] [2880,960,180,20,1] [1,80,360,720,2880] Bessel-Triangle k = -1 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 2 [1,1] [1,1] [1,1] 8 [1,3,4] [4,3,1] [1,3,4] 62 [1,6,3,16,36] [36,19,6,1] [1,9,16,36] 862 [1,10,15,40,40,180,576] [576,220,55,10,1] [1,25,80,180,576] Bessel-Triangle k = 0 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 1 [1,0] [0,1] [1,0] 1 [1,0,0] [0,0,1] [1,0,0] 1 [1,0,0,0,0] [0,0,0,1] [1,0,0,0] 1 [1,0,0,0,0,0,0] [0,0,0,0,1] [1,0,0,0,0] Bessel-Triangle k = 1 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 2 [1,1] [1,1] [1,1] 4 [1,3,0] [0,3,1] [1,3,0] 10 [1,6,3,0,0] [0,3,6,1] [1,9,0,0] 26 [1,10,15,0,0,0,0] [0,0,15,10,1] [1,25,0,0,0] Bessel-Triangle k = 2 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 3 [1,2] [2,1] [1,2] 11 [1,6,4] [4,6,1] [1,6,4] 41 [1,12,12,16,0] [0,28,12,1] [1,24,16,0] 201 [1,20,60,40,80,0,0] [0,80,100,20,1] [1,80,120,0,0] Bessel-Triangle k = 3 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 4 [1,3] [3,1] [1,3] 22 [1,9,12] [12,9,1] [1,9,12] 130 [1,18,27,48,36] [36,75,18,1] [1,45,48,36] 826 [1,30,135,120,360,180,0] [0,540,255,30,1] [1,165,480,180,0] Bessel-Triangle k = 4 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 5 [1,4] [4,1] [1,4] 37 [1,12,24] [24,12,1] [1,12,24] 313 [1,24,48,96,144] [144,144,24,1] [1,72,96,144] 2777 [1,40,240,240,960,720,576] [576,1680,480,40,1] [1,280,1200,720,576] Bessel-Triangle k = 5 sum all partitions ~ by length ~ by biggest part 1 [1] [1] [1] 1 [1] [1] [1] 6 [1,5] [5,1] [1,5] 56 [1,15,40] [40,15,1] [1,15,40] 626 [1,30,75,160,360] [360,235,30,1] [1,105,160,360] 7506 [1,50,375,400,2000,1800,2880] [2880,3800,775,50,1] [1,425,2400,1800,2880]