A155812 Triangle, read by rows, where g.f.: A(x,y) = exp( Sum_{n>=1} (3^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

1, 3, 1, 45, 12, 1, 6687, 801, 39, 1, 10782369, 540720, 10764, 120, 1, 169490304819, 3499254081, 29275956, 129348, 363, 1, 25016281429306077, 206071208583660, 709664882337, 1321144632, 1459773, 1092, 1, 34185693516532070487615

Offset: 0

Author

Paul D. Hanna, Feb 04 2009

Keywords

• nonn
• tabl

Comments

More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

Examples

			G.f.: A(x,y) = 1 + (3 + y)x + (45 + 12y + y^2)x^2 + (6687 + 801y + 39y^2 + y^3)x^3 +...
Triangle begins:
1;
3, 1;
45, 12, 1;
6687, 801, 39, 1;
10782369, 540720, 10764, 120, 1;
169490304819, 3499254081, 29275956, 129348, 363, 1;
25016281429306077, 206071208583660, 709664882337, 1321144632, 1459773, 1092, 1;
34185693516532070487615, 109444624780070083617, 150302858159634327, 115097787387369, 53628299415, 15815241, 3279, 1; ...
		

Crossrefs

Cf. A155203 (column 0), A155204 (row sums), A155813 (column 1).

Programs

PARI

{T(n,k)=polcoeff(polcoeff(exp(sum(m=1,n+1,(3^m+y)^m*x^m/m)+x*O(x^n)),n,x),k,y)}

Formula

G.f.: A(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k.