A384583 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 A384575.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 6, 0, 1, 4, 6, 14, 31, 0, 1, 5, 10, 25, 75, 236, 0, 1, 6, 15, 40, 135, 546, 2166, 0, 1, 7, 21, 60, 215, 951, 4902, 22722, 0, 1, 8, 28, 86, 320, 1476, 8338, 50620, 269889, 0, 1, 9, 36, 119, 456, 2151, 12634, 84714, 593347, 3567412, 0

Offset

0,8

Links

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

Formula

A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(5*n-5*j+k,j)/(5*n-5*j+k) * A(n-j,j).

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,    6,   14,   25,    40,    60,    86, ...
  0,   31,   75,  135,   215,   320,   456, ...
  0,  236,  546,  951,  1476,  2151,  3012, ...
  0, 2166, 4902, 8338, 12634, 17985, 24627, ...

Prog

(PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(5*n-5*j+k, j)/(5*n-5*j+k)*a(n-j, j)));

Crossrefs

Columns k=0..1 give A000007, A384575.

Cf. A381566, A384580, A384581, A384582.

Sequence in context: A384866 A384581 A384582 * A353436 A286932 A350364

Adjacent sequences: A384580 A384581 A384582 * A384584 A384585 A384586

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 04 2025

Status

approved