A384741 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 A384739.

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 28, 0, 1, 4, 15, 74, 461, 0, 1, 5, 24, 144, 1200, 11776, 0, 1, 6, 35, 244, 2325, 29842, 421207, 0, 1, 7, 48, 380, 3968, 56688, 1040896, 19832128, 0, 1, 8, 63, 558, 6285, 95524, 1933227, 47948490, 1179482201, 0

Offset

0,8

Links

Table of n, a(n) for n=0..54.

Formula

A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} (2*n-2*j+k)^(j-1) * binomial(n,j) * A(n-j,j).

Example

Square array begins:
  1,     1,     1,     1,     1,      1, ...
  0,     1,     2,     3,     4,      5, ...
  0,     3,     8,    15,    24,     35, ...
  0,    28,    74,   144,   244,    380, ...
  0,   461,  1200,  2325,  3968,   6285, ...
  0, 11776, 29842, 56688, 95524, 150400, ...

Prog

(PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (2*n-2*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));

Crossrefs

Columns k=0..1 give A000007, A384739.

Cf. A380178, A384742.

Sequence in context: A384802 A380178 A384804 * A384742 A305401 A396446

Adjacent sequences: A384738 A384739 A384740 * A384742 A384743 A384744

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 08 2025

Status

approved