A221971 G.f.: A(x,y) = Sum_{n>=0} n! * x^n*y^n * Product_{k=1..n} (1 + k*x) / (1 + k*x*y + k^2*x^2*y).

1, 0, 1, 0, 1, 1, 0, 0, 4, 1, 0, 0, 3, 11, 1, 0, 0, 0, 27, 26, 1, 0, 0, 0, 17, 148, 57, 1, 0, 0, 0, 0, 278, 646, 120, 1, 0, 0, 0, 0, 155, 2590, 2481, 247, 1, 0, 0, 0, 0, 0, 4073, 18304, 8805, 502, 1, 0, 0, 0, 0, 0, 2073, 58427, 109699, 29682, 1013, 1, 0, 0, 0

Offset: 0

Author

Paul D. Hanna, Feb 01 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
0, 1;
0, 1, 1;
0, 0, 4, 1;
0, 0, 3, 11, 1;
0, 0, 0, 27, 26, 1;
0, 0, 0, 17, 148, 57, 1;
0, 0, 0, 0, 278, 646, 120, 1;
0, 0, 0, 0, 155, 2590, 2481, 247, 1;
0, 0, 0, 0, 0, 4073, 18304, 8805, 502, 1;
0, 0, 0, 0, 0, 2073, 58427, 109699, 29682, 1013, 1;
0, 0, 0, 0, 0, 0, 80712, 614819, 590254, 96648, 2036, 1;
0, 0, 0, 0, 0, 0, 38227, 1665829, 5340996, 2948040, 307255, 4083, 1; ...
		

Links

• Paul D. Hanna, Rows n = 0..32, flattened.

Crossrefs

Cf. A208237 (row sums), A110501 (central terms), A005439 (column sums), A136126.

Programs

PARI

{T(n,k)=polcoeff(polcoeff(sum(m=0, n,m!*x^m*y^m*prod(k=1, m, (1+k*x)/(1+k*x*y+k^2*x^2*y +x*O(x^n)))),n,x),k,y)}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))

Formula

Row sums equal A208237.

Central terms equal A110501, the Genocchi numbers of first kind (unsigned).

Columns sums equal A005439, the Genocchi numbers of second kind.