A355423 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{j=1..k} (exp(j*x) - 1)).

1, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 6, 14, 5, 0, 1, 10, 50, 81, 15, 0, 1, 15, 130, 504, 551, 52, 0, 1, 21, 280, 2000, 5870, 4266, 203, 0, 1, 28, 532, 6075, 35054, 76872, 36803, 877, 0, 1, 36, 924, 15435, 148429, 684000, 1111646, 348543, 4140, 0

Offset

0,8

Links

Table of n, a(n) for n=0..54.

Formula

T(0,k) = 1 and T(n,k) = Sum_{i=1..n} (Sum_{j=1..k} j^i) * binomial(n-1,i-1) * T(n-i,k) for n > 0.

Example

Square array begins:
  1,  1,    1,     1,      1,       1, ...
  0,  1,    3,     6,     10,      15, ...
  0,  2,   14,    50,    130,     280, ...
  0,  5,   81,   504,   2000,    6075, ...
  0, 15,  551,  5870,  35054,  148429, ...
  0, 52, 4266, 76872, 684000, 4004100, ...

Crossrefs

Columns k=0-4 give: A000007, A000110, A355291, A355421, A355422.

Main diagonal gives A320288.

Cf. A306024, A320253.

Sequence in context: A292717 A365727 A054654 * A345066 A253669 A154477

Adjacent sequences: A355420 A355421 A355422 * A355424 A355425 A355426

Keyword

nonn,tabl

Author

Seiichi Manyama, Jul 01 2022

Status

approved