A379598 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 A110447.

1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 6, 0, 1, 4, 9, 16, 23, 0, 1, 5, 14, 31, 62, 104, 0, 1, 6, 20, 52, 123, 278, 531, 0, 1, 7, 27, 80, 213, 552, 1398, 2982, 0, 1, 8, 35, 116, 340, 964, 2750, 7718, 18109, 0, 1, 9, 44, 161, 513, 1561, 4784, 14976, 46083, 117545, 0

Offset

0,8

Links

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

Formula

See A030266.

Example

Square array begins:
  1,   1,    1,    1,    1,    1,     1, ...
  0,   1,    2,    3,    4,    5,     6, ...
  0,   2,    5,    9,   14,   20,    27, ...
  0,   6,   16,   31,   52,   80,   116, ...
  0,  23,   62,  123,  213,  340,   513, ...
  0, 104,  278,  552,  964, 1561,  2400, ...
  0, 531, 1398, 2750, 4784, 7755, 11987, ...

Prog

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

Crossrefs

Columns k=0..1 give A000007, A110447 (A030266(n+1)).

Cf. A379599, A380178.

Sequence in context: A130020 A292870 A378291 * A306704 A384626 A384651

Adjacent sequences: A379595 A379596 A379597 * A379599 A379600 A379601

Keyword

nonn,tabl

Author

Seiichi Manyama, Feb 27 2025

Status

approved