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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 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 A332238 A192887 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 May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)