OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..450
Eric Weisstein's World of Mathematics, Laguerre Polynomial.
FORMULA
a(n) ~ exp(2*sqrt(n) - 1/2) * n^(3/4) / (2*sqrt(Pi)) * (1 + 31/(48*sqrt(n))). - Vaclav Kotesovec, Nov 14 2017
a(n) = round(n * [x^n] exp(x/(1 - x))/(1 - x)). - Ilya Gutkovskiy, Jun 05 2018
a(n) = round(n * Sum_{k=0..n} binomial(n, k) / k!). - Sean A. Irvine, Jun 01 2024
MAPLE
a := n->round(expand(n*LaguerreL(n, -1)));
MATHEMATICA
a[n_] := Round[n*LaguerreL[n, 0, -1]]
PROG
(PARI) {a(n) = if( n<0, 0, round(n * polcoeff(exp(x/(1-x) + x*O(x^n)) / (1-x), n)))}; /* Michael Somos, Dec 04 2002 */
(PARI) for(n=0, 40, print1(round(n*sum(k=0, n, binomial(n, k)/k!)), ", ")) \\ G. C. Greubel, May 14 2018
(Magma) [Round(n*(&+[Binomial(n, k)/Factorial(k): k in [0..n]])): n in [0..40]]; // G. C. Greubel, May 14 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Apr 19 2002
STATUS
approved