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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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: A307803 A136517 A104097 * A158958 A098341 A223173

Adjacent sequences:  A155809 A155810 A155811 * A155813 A155814 A155815

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Feb 04 2009

STATUS

approved

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Last modified July 23 01:27 EDT 2019. Contains 325228 sequences. (Running on oeis4.)