A221987 G.f.: A(x,y) = Sum_{n>=0} n!*x^n*y^n * Product_{k=1..n} (1+y + 2*k*x*y) / (1 + (1+y)*k*x + 2*k^2*x^2*y).

1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 62, 26, 1, 1, 57, 274, 274, 57, 1, 1, 120, 1063, 2024, 1063, 120, 1, 1, 247, 3805, 12411, 12411, 3805, 247, 1, 1, 502, 12916, 67882, 113414, 67882, 12916, 502, 1, 1, 1013, 42284, 343700, 891930, 891930, 343700, 42284, 1013, 1

Offset: 0

Author

Paul D. Hanna, Feb 02 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
1, 1;
1, 4, 1;
1, 11, 11, 1;
1, 26, 62, 26, 1;
1, 57, 274, 274, 57, 1;
1, 120, 1063, 2024, 1063, 120, 1;
1, 247, 3805, 12411, 12411, 3805, 247, 1;
1, 502, 12916, 67882, 113414, 67882, 12916, 502, 1;
1, 1013, 42284, 343700, 891930, 891930, 343700, 42284, 1013, 1;
1, 2036, 134981, 1646808, 6339786, 9718184, 6339786, 1646808, 134981, 2036, 1; ...
		

Links

• Paul D. Hanna, Rows n=0..31, flattened.

Crossrefs

Cf. A221988, A136126, A221971.

Programs

PARI

{T(n, k)=polcoeff(polcoeff( sum(m=0, n, m!*x^m*prod(k=1, m, (1+y+2*k*x*y)/(1+(1+y)*k*x+2*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 A221988.