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A277423 a(n) = n!*LaguerreL(n, n). 14
1, 0, -2, 6, 24, -380, 720, 31794, -361088, -2104056, 101548800, -612792290, -25534891008, 593660731404, 2831189530624, -361541172525750, 4481749181890560, 169464194149739536, -6805365045197340672, -9663483091971306186, 6883830206467440640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..415

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

FORMULA

a(n) = n! * Sum_{k=0..n} binomial(n, k) * (-1)^k * n^k / k!.

a(n) = n! * [x^n] exp(-n*x/(1 - x))/(1 - x). - Ilya Gutkovskiy, Nov 21 2017

MATHEMATICA

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

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

Table[n! * Hypergeometric1F1[-n, 1, n], {n, 0, 20}] (* Vaclav Kotesovec, Feb 20 2020 *)

PROG

(PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n, k)*(-1)^k*n^k/k!), ", ")) \\ G. C. Greubel, May 16 2018

(MAGMA) [Factorial(n)*(&+[Binomial(n, k)*(-1)^k*n^k/Factorial(k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, May 16 2018

CROSSREFS

Cf. A277373, A277391, A277392, A277418, A277419, A277420, A277421, A277422.

Cf. A002720, A087912, A277382.

Sequence in context: A292751 A274098 A324141 * A191460 A073475 A000805

Adjacent sequences:  A277420 A277421 A277422 * A277424 A277425 A277426

KEYWORD

sign

AUTHOR

Vaclav Kotesovec, Oct 14 2016

STATUS

approved

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)