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A155812
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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.
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5
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f.: A(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k.
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EXAMPLE
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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; ...
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PROG
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(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)}
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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