A381602 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A120971.

1, 1, 0, 1, 1, 0, 1, 2, 4, 0, 1, 3, 9, 26, 0, 1, 4, 15, 60, 218, 0, 1, 5, 22, 103, 504, 2151, 0, 1, 6, 30, 156, 870, 4946, 23854, 0, 1, 7, 39, 220, 1329, 8511, 54430, 289555, 0, 1, 8, 49, 296, 1895, 12988, 93070, 655362, 3783568, 0, 1, 9, 60, 385, 2583, 18536, 141316, 1112382, 8496454, 52624689, 0

Offset

0,8

Links

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

Formula

See A120971.

Example

Square array begins:
  1,     1,     1,     1,      1,      1,      1, ...
  0,     1,     2,     3,      4,      5,      6, ...
  0,     4,     9,    15,     22,     30,     39, ...
  0,    26,    60,   103,    156,    220,    296, ...
  0,   218,   504,   870,   1329,   1895,   2583, ...
  0,  2151,  4946,  8511,  12988,  18536,  25332, ...
  0, 23854, 54430, 93070, 141316, 200930, 273915, ...

Prog

(PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n+k, j)/(2*n+k)*a(n-j, 2*j)));

Crossrefs

Columns k=0..1 give A000007, A120971.

Cf. A379598, A381603.

Sequence in context: A378323 A378290 A118343 * A309148 A351761 A226031

Adjacent sequences: A381599 A381600 A381601 * A381603 A381604 A381605

Keyword

nonn,tabl

Author

Seiichi Manyama, Mar 01 2025

Status

approved