OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..335
Eric Weisstein's World of Mathematics, Laguerre Polynomial
Wikipedia, Laguerre polynomials
FORMULA
a(n) = n! * [x^n] exp(n*x/(1 - x))/(1 - x)^(n+1).
a(n) = n!*Laguerre(n,n,-n).
a(n) ~ 2^(n - 1/2) * (1 + sqrt(2))^(n + 1/2) * n^n / exp((2 - sqrt(2))*n). - Vaclav Kotesovec, Nov 21 2017
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n x/(1 - x)]/(1 - x)^(n + 1), {x, 0, n}], {n, 0, 17}]
Table[n! LaguerreL[n, n, -n], {n, 0, 17}]
Table[(-1)^n HypergeometricU[-n, n + 1, -n], {n, 0, 17}]
Join[{1}, Table[n! Sum[Binomial[2 n, n - k] n^k/k!, {k, 0, n}], {n, 1, 17}]]
PROG
(PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(2*n, n-k)*n^k/k!), ", ")) \\ G. C. Greubel, Feb 06 2018
(Magma) [Factorial(n)*(&+[Binomial(2*n, n-k)*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 21 2017
STATUS
approved