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A332694
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a(n) = (-1)^n * n! * Laguerre(n, 5*n).
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5
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1, 4, 62, 1614, 58904, 2764880, 158631120, 10755909010, 841471425920, 74605812325020, 7392555309228800, 809594650092540950, 97103822900059929600, 12659189667284189060200, 1782335176686080469555200, 269524635118213823349788250, 43567606796796836119605248000
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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) ~ exp((3-sqrt(5))*n/2) * ((sqrt(5) + 1)/2)^(2*n+1) * n^n / 5^(1/4). - Vaclav Kotesovec, Feb 20 2020, simplified May 09 2021
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MATHEMATICA
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Table[(-1)^n * n! * LaguerreL[n, 5*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k] * (-1)^(n-k) * 5^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]
Table[(-1)^n * n! * Hypergeometric1F1[-n, 1, 5*n], {n, 0, 20}]
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PROG
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(PARI) a(n) = (-1)^n*n!*pollaguerre(n, 0, 5*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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