A381569 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 A381570.

1, 1, 0, 1, 3, 0, 1, 6, 12, 0, 1, 9, 33, 82, 0, 1, 12, 63, 236, 732, 0, 1, 15, 102, 489, 2100, 7944, 0, 1, 18, 150, 868, 4428, 22248, 99156, 0, 1, 21, 207, 1400, 8121, 46422, 270268, 1381464, 0, 1, 24, 273, 2112, 13665, 85272, 552540, 3668568, 21065853, 0

Offset

0,5

Links

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

Formula

A(n,0) = 0^n; A(n,k) = k * Sum_{j=0..n} binomial(3*n-3*j+3*k,j)/(n-j+k) * A(n-j,j).

Example

Square array begins:
  1,    1,     1,     1,     1,      1, ...
  0,    3,     6,     9,    12,     15, ...
  0,   12,    33,    63,   102,    150, ...
  0,   82,   236,   489,   868,   1400, ...
  0,  732,  2100,  4428,  8121,  13665, ...
  0, 7944, 22248, 46422, 85272, 145143, ...

Prog

(PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-3*j+3*k, j)/(n-j+k)*a(n-j, j)));

Crossrefs

Columns k=0..1 give A000007, A381570.

Cf. A381566, A381567.

Sequence in context: A243984 A100485 A143397 * A341856 A339350 A381573

Adjacent sequences: A381566 A381567 A381568 * A381570 A381571 A381572

Keyword

nonn,tabl

Author

Seiichi Manyama, Feb 28 2025

Status

approved