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A332679
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a(n) = (-1)^n * n! * Laguerre(n, 4*n).
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9
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1, 3, 34, 642, 16920, 571880, 23577552, 1147008912, 64304389504, 4081584090240, 289302692908800, 22648001532831488, 1940655970832219136, 180654087647513945088, 18153823412468554639360, 1958590905998560664832000, 225799980396482832660529152, 27702168947661388727726931968
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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) ~ c * n^(n + 1/6) * exp(n), where c = Gamma(1/3) / (2^(5/6) * 3^(1/6) * sqrt(Pi)) = 0.706332637459...
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MATHEMATICA
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Table[(-1)^n*n!*LaguerreL[n, 4*n], {n, 0, 20}]
Join[{1}, Table[n! * Sum[(-1)^(n-k) * Binomial[n, k] * (4*n)^k/k!, {k, 0, n}], {n, 1, 20}]]
Table[(-1)^n*n!*Hypergeometric1F1[-n, 1, 4*n], {n, 0, 20}]
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PROG
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(PARI) a(n) = (-1)^n*n!*pollaguerre(n, 0, 4*n); \\ Michel Marcus, Feb 05 2021
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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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