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A218143
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a(n) = Stirling2(n*(n+1)/2, n).
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3
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1, 1, 3, 90, 34105, 210766920, 26585679462804, 82892803728383735268, 7529580759157036060608585183, 22982258052528294182955639980819773510, 2672446997421818663856559987803834697952486978300, 13239043631590111512460321918828937597837325561187113535696980
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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*(n-1)/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 + 3*x^2 + 90*x^3 + 34105*x^4 + 210766920*x^5 + 26585679462804*x^6 +...
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MATHEMATICA
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PROG
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(PARI) {a(n)=polcoeff(1/prod(k=1, n, 1-k*x +x*O(x^(n*(n-1)/2))), n*(n-1)/2)}
(PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n) = Stirling2(n*(n+1)/2, n)}
for(n=0, 15, print1(a(n), ", "))
(Maxima) makelist(stirling2(n*(n+1)/2, 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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