A380178 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A162659.

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 22, 0, 1, 4, 15, 62, 281, 0, 1, 5, 24, 126, 792, 5396, 0, 1, 6, 35, 220, 1641, 14922, 142297, 0, 1, 7, 48, 350, 2960, 30708, 384316, 4865806, 0, 1, 8, 63, 522, 4905, 55604, 777537, 12836406, 207407489, 0, 1, 9, 80, 742, 7656, 93300, 1393720, 25450806, 535396784, 10710044776, 0

Offset

0,8

Links

Table of n, a(n) for n=0..65.

Formula

See A162659.

Example

Square array begins:
  1,      1,      1,      1,       1,       1,       1, ...
  0,      1,      2,      3,       4,       5,       6, ...
  0,      3,      8,     15,      24,      35,      48, ...
  0,     22,     62,    126,     220,     350,     522, ...
  0,    281,    792,   1641,    2960,    4905,    7656, ...
  0,   5396,  14922,  30708,   55604,   93300,  148446, ...
  0, 142297, 384316, 777537, 1393720, 2330305, 3716532, ...

Prog

(PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, j)));

Crossrefs

Columns k=0..1 give A000007, A162659.

Cf. A379168.

Sequence in context: A396412 A396992 A384802 * A384804 A384741 A384742

Adjacent sequences: A380175 A380176 A380177 * A380179 A380180 A380181

Keyword

nonn,tabl

Author

Seiichi Manyama, Feb 11 2025

Status

approved