A384752 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 A384750.

1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 154, 0, 1, 4, 27, 350, 5977, 0, 1, 5, 40, 594, 13480, 351196, 0, 1, 6, 55, 892, 22761, 783722, 28315369, 0, 1, 7, 72, 1250, 34096, 1311228, 62574580, 2954632402, 0, 1, 8, 91, 1674, 47785, 1949044, 103734513, 6473363654, 383525186209, 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} (3*n-3*j+k)^(j-1) * binomial(n,j) * A(n-j,3*j).

Example

Square array begins:
  1,      1,      1,       1,       1,       1, ...
  0,      1,      2,       3,       4,       5, ...
  0,      7,     16,      27,      40,      55, ...
  0,    154,    350,     594,     892,    1250, ...
  0,   5977,  13480,   22761,   34096,   47785, ...
  0, 351196, 783722, 1311228, 1949044, 2714300, ...

Prog

(PARI) a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (3*n-3*j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));

Crossrefs

Columns k=0..1 give A000007, A384750.

Sequence in context: A384722 A384862 A384788 * A396500 A396501 A199292

Adjacent sequences: A384749 A384750 A384751 * A384753 A384754 A384755

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 09 2025

Status

approved