A381603 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 A120973.

1, 1, 0, 1, 1, 0, 1, 2, 6, 0, 1, 3, 13, 60, 0, 1, 4, 21, 132, 776, 0, 1, 5, 30, 217, 1708, 11802, 0, 1, 6, 40, 316, 2814, 25876, 201465, 0, 1, 7, 51, 430, 4113, 42510, 439446, 3759100, 0, 1, 8, 63, 560, 5625, 62016, 718647, 8155874, 75404151, 0, 1, 9, 76, 707, 7371, 84731, 1044228, 13270944, 162762498, 1608036861, 0

Offset

0,8

Links

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

Formula

See A120973.

Example

Square array begins:
  1,      1,      1,      1,       1,       1,       1, ...
  0,      1,      2,      3,       4,       5,       6, ...
  0,      6,     13,     21,      30,      40,      51, ...
  0,     60,    132,    217,     316,     430,     560, ...
  0,    776,   1708,   2814,    4113,    5625,    7371, ...
  0,  11802,  25876,  42510,   62016,   84731,  111018, ...
  0, 201465, 439446, 718647, 1044228, 1421835, 1857631, ...

Prog

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

Crossrefs

Columns k=0..1 give A000007, A120973.

Cf. A379598, A381602.

Sequence in context: A384946 A118354 A384621 * A396995 A080730 A232178

Adjacent sequences: A381600 A381601 A381602 * A381604 A381605 A381606

Keyword

nonn,tabl

Author

Seiichi Manyama, Mar 01 2025

Status

approved