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A277419 a(n) = n!*LaguerreL(n, -5*n). 11
1, 6, 142, 5676, 318744, 23046370, 2038090320, 213094791840, 25714702990720, 3517403388684030, 537798502938028800, 90890936781714193300, 16825134146527678233600, 3385560150770468257273050, 735772370353606135149107200, 171753027520961356975091493000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..250

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

FORMULA

a(n) = n! * Sum_{k=0..n} binomial(n, k) * 5^k * n^k / k!.

a(n) ~ sqrt(1/2 + 7/(6*sqrt(5))) * ((7 + 3*sqrt(5))/2)^n * exp((-7 + 3*sqrt(5))*n/2) * n^n.

MATHEMATICA

Table[n!*LaguerreL[n, -5*n], {n, 0, 20}]

Flatten[{1, Table[n!*Sum[Binomial[n, k] * 5^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]

PROG

(PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n, k)*5^k*n^k/k!), ", ")) \\ G. C. Greubel, May 15 2018

(MAGMA) [Factorial(n)*(&+[Binomial(n, k)*5^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 15 2018

CROSSREFS

Cf. A277373, A277391, A277392, A277418, A277420, A277421, A277422.

Cf. A002720, A087912, A277382.

Sequence in context: A286446 A048863 A278356 * A111839 A037049 A196811

Adjacent sequences:  A277416 A277417 A277418 * A277420 A277421 A277422

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 14 2016

STATUS

approved

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Last modified June 12 14:45 EDT 2021. Contains 344957 sequences. (Running on oeis4.)