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A192552
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a(n) = sum(stirling2(n,k)*(-1)^(n-k)*k!^2,k=0..n).
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0
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1, 1, 3, 25, 387, 9481, 336723, 16340185, 1038177507, 83616187561, 8323660051443, 1003415542660345, 144043181112445827, 24279259683302736841, 4747993384270354742163, 1066206704980940216628505, 272480888391150986151565347
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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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O.g.f.: Sum_{n>=0} n!^2 * x^n / Product_{k=0..n} (1 + k*x). [From Paul D. Hanna, Jul 20 2011]
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MATHEMATICA
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Table[Sum[StirlingS2[n, k](-1)^(n-k)k!^2, {k, 0, n}], {n, 0, 100}]
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PROG
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(Maxima) makelist(sum(stirling2(n, k)*(-1)^(n-k)*k!^2, k, 0, n), n, 0, 24);
(PARI) {a(n)=polcoeff(sum(m=0, n, m!^2*x^m/prod(k=1, m, 1+k*x+x*O(x^n))), n)} /* Paul D. Hanna, Jul 20 2011 */
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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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