OFFSET
0,3
COMMENTS
Appears to be a transposed version of A188553 with a leading column of 1's.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
FORMULA
T(n,k) = A193605(n,k).
T(n,m) = Sum_{k=1..m} k*binomial(n,m-k). - Vladimir Kruchinin, Apr 06 2018
EXAMPLE
Table starts:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1, 3, 5, 7, 9, 11, 13, 15, 17, 19
1, 4, 8, 12, 16, 20, 24, 28, 32, 36
1, 5, 12, 20, 28, 36, 44, 52, 60, 68
1, 6, 17, 32, 48, 64, 80, 96, 112, 128
1, 7, 23, 49, 80, 112, 144, 176, 208, 240
1, 8, 30, 72, 129, 192, 256, 320, 384, 448
1, 9, 38, 102, 201, 321, 448, 576, 704, 832
1, 10, 47, 140, 303, 522, 769, 1024, 1280, 1536
1, 11, 57, 187, 443, 825, 1291, 1793, 2304, 2816
1, 12, 68, 244, 630, 1268, 2116, 3084, 4097, 5120
1, 13, 80, 312, 874, 1898, 3384, 5200, 7181, 9217
1, 14, 93, 392, 1186, 2772, 5282, 8584, 12381, 16398
1, 15, 107, 485, 1578, 3958, 8054, 13866, 20965, 28779
1, 16, 122, 592, 2063, 5536, 12012, 21920, 34831, 49744
1, 17, 138, 714, 2655, 7599, 17548, 33932, 56751, 84575
1, 18, 155, 852, 3369, 10254, 25147, 51480, 90683, 141326
1, 19, 173, 1007, 4221, 13623, 35401, 76627, 142163, 232009
1, 20, 192, 1180, 5228, 17844, 49024, 112028, 218790, 374172
1, 21, 212, 1372, 6408, 23072, 66868, 161052, 330818, 592962
1, 22, 233, 1584, 7780, 29480, 89940, 227920, 491870, 923780
1, 23, 255, 1817, 9364, 37260, 119420, 317860, 719790,1415650
1, 24, 278, 2072, 11181, 46624, 156680, 437280,1037650,2135440
1, 25, 302, 2350, 13253, 57805, 203304, 593960,1474930,3173090
1, 26, 327, 2652, 15603, 71058, 261109, 797264,2068890,4648020
1, 27, 353, 2979, 18255, 86661, 332167,1058373,2866154,6716910
1, 28, 380, 3332, 21234, 104916, 418828,1390540,3924527,9583064
PROG
(PARI) T(n, m) = {sum(k=1, m, k*binomial(n, m-k))}
{ for(n=0, 10, for(m=1, 10, print1(T(n, m), ", ")); print) } \\ Andrew Howroyd, Apr 28 2020
CROSSREFS
KEYWORD
AUTHOR
Jakub Jaroslaw Ciaston, Jan 23 2013
EXTENSIONS
Offset corrected and terms a(55) and beyond from Andrew Howroyd, Apr 28 2020
STATUS
approved