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A277420
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a(n) = n!*LaguerreL(n, -6*n).
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11
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1, 7, 194, 9078, 596760, 50508120, 5228520912, 639915545808, 90390815432064, 14472947716917120, 2590274418097708800, 512433683486806447872, 111036605823697437490176, 26153418409614396515976192, 6653213794092052464421939200, 1817951594633556391548903168000
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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) * 6^k * n^k / k!.
a(n) ~ sqrt(1/2 + 2/sqrt(15)) * (4 + sqrt(15))^n * exp((-4 + sqrt(15))*n) * n^n.
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MATHEMATICA
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Table[n!*LaguerreL[n, -6*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k] * 6^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)*6^k*n^k/k!), ", ")) \\ G. C. Greubel, May 15 2018
(Magma) [Factorial(n)*(&+[Binomial(n, k)*6^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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