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A289211 a(n) = n! * Laguerre(n,-5). 4
1, 6, 47, 446, 4929, 61870, 866695, 13373190, 224995745, 4094022230, 80031878175, 1671426609550, 37116087808225, 872797202471550, 21656891639499575, 565266064058561750, 15476777687220818625, 443409439715399299750, 13263588837009155407375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..435

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

FORMULA

E.g.f.: exp(5*x/(1-x))/(1-x).

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

a(n) = n! * A160609(n)/A160610(n).

a(n) ~ exp(-5/2 + 2*sqrt(5*n) - n) * n^(n + 1/4) / (sqrt(2)*5^(1/4)) * (1 + 223/(48*sqrt(5*n))). - Vaclav Kotesovec, Nov 13 2017

MAPLE

a:= n-> n! * add(binomial(n, i)*5^i/i!, i=0..n):

seq(a(n), n=0..20);

MATHEMATICA

[Table[n!*LaguerreL[n, -5], {n, 0, 50}]] (* G. C. Greubel, May 09 2018 *)

PROG

(PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n, k)*(5^k/k!)), ", ")) \\ G. C. Greubel, May 09 2018

(MAGMA) [(Factorial(n)*(&+[Binomial(n, k)*(5^k/Factorial(k)): k in [0..n]])): n in [0..30]]; // G. C. Greubel, May 09 2018

CROSSREFS

Column k=5 of A289192.

Cf. A160609, A160610.

Sequence in context: A291028 A071878 A104256 * A307567 A192887 A321190

Adjacent sequences:  A289208 A289209 A289210 * A289212 A289213 A289214

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 28 2017

STATUS

approved

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Last modified September 21 22:17 EDT 2019. Contains 327284 sequences. (Running on oeis4.)