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

0,2

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.

Links

Table of n, a(n) for n=0..28.

Formula

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

Example

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; ...

Prog

(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)}

Crossrefs

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

Sequence in context: A366479 A104097 A344379 * A158958 A098341 A354391

Adjacent sequences: A155809 A155810 A155811 * A155813 A155814 A155815

Keyword

nonn,tabl

Author

Paul D. Hanna, Feb 04 2009

Status

approved