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A277392
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a(n) = n!*LaguerreL(n, -3*n).
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11
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1, 4, 62, 1626, 59928, 2844120, 165100752, 11331597942, 897635712384, 80602042275756, 8090067511468800, 897561658361441106, 109072492644378442752, 14407931244544181001216, 2055559499598438969956352, 314997663481165477898736750, 51601245736595962597616222208
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..n} binomial(n, k) * 3^k * n^k / k!.
a(n) ~ sqrt(1/2+5/(2*sqrt(21))) * (5+sqrt(21))^n * exp(n*(sqrt(21)-5)/2) * n^n/2^n.
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MATHEMATICA
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Table[n!*LaguerreL[n, -3*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k]*3^k*n^k/k!, {k, 0, n}], {n, 1, 20}]}]
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PROG
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(PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n, k)*3^k*n^k/k!), ", ")) \\ G. C. Greubel, May 15 2018
(Magma) [Factorial(n)*(&+[Binomial(n, k)*3^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 15 2018
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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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