A381566 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 A087949.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 2, 0, 1, 4, 6, 6, 5, 0, 1, 5, 10, 13, 15, 16, 0, 1, 6, 15, 24, 33, 46, 59, 0, 1, 7, 21, 40, 63, 99, 164, 246, 0, 1, 8, 28, 62, 110, 188, 343, 662, 1131, 0, 1, 9, 36, 91, 180, 331, 638, 1344, 2961, 5655, 0

Offset

0,8

Links

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

Formula

See A087949.

Example

Square array begins:
  1,  1,   1,   1,   1,    1,    1, ...
  0,  1,   2,   3,   4,    5,    6, ...
  0,  1,   3,   6,  10,   15,   21, ...
  0,  2,   6,  13,  24,   40,   62, ...
  0,  5,  15,  33,  63,  110,  180, ...
  0, 16,  46,  99, 188,  331,  552, ...
  0, 59, 164, 343, 638, 1110, 1845, ...

Prog

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

Crossrefs

Columns k=0..1 give A000007, A087949.

Cf. A379598, A381567, A381569.

Sequence in context: A291652 A378320 A384864 * A071569 A378321 A384865

Adjacent sequences: A381563 A381564 A381565 * A381567 A381568 A381569

Keyword

nonn,tabl

Author

Seiichi Manyama, Feb 28 2025

Status

approved