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A218142
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a(n) = Stirling2(n^2+n, n).
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3
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1, 1, 31, 86526, 45232115901, 7713000216608565075, 666480349285726891499539272955, 41929298560838945526242744414099901692285884, 2610516895723221966171633379256064857587637240616032299710417
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = [x^n] Sum_{k>=0} k^((n+1)*k) * exp(-k^(n+1)*x) * x^k / k!.
a(n) = [x^(n^2)] 1 / Product_{k=1..n} (1-k*x).
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EXAMPLE
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O.g.f.: A(x) = 1 + x + 31*x^2 + 86526*x^3 + 45232115901*x^4 +...
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MATHEMATICA
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PROG
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(PARI) {a(n)=polcoeff(sum(k=0, n, (k^(n+1))^k*exp(-k^(n+1)*x +x*O(x^n))*x^k/k!), n)}
(PARI) {a(n)=polcoeff(1/prod(k=1, n, 1-k*x +x*O(x^(n^2))), n^2)}
(PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n) = Stirling2(n^2+n, n)}
for(n=0, 10, print1(a(n), ", "))
(Maxima) makelist(stirling2(n^2+n, n), n, 0, 30 ); /* Martin Ettl, Oct 21 2012 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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