OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..440
FORMULA
a(n) = Sum_{k=1..n} (n!^2 / k!*(n-k)!^2).
a(n) = Sum_{k=1..n} P(n, k)*C(n, k) where P(n,k), are the permutation coefficients A008279.
a(n) = n * A129833(n-1) for n>=1. - Peter Luschny, Oct 11 2016
From G. C. Greubel, Aug 11 2022: (Start)
E.g.f.: exp(x/(1-x))/(1-x) - exp(x).
Sum_{n >= 0} a(n)*x^n/(n!)^2 = (exp(x) -1)*BesselI(0, 2*sqrt(x)). (End)
MAPLE
a := n -> hypergeom([-n, -n], [], 1) - 1:
seq(simplify(a(n)), n=0..26); # Peter Luschny, Oct 11 2016
MATHEMATICA
Table[n!*LaguerreL[n, -1] -1, {n, 0, 40}] (* G. C. Greubel, Aug 11 2022 *)
PROG
(Magma) [Factorial(n)*Evaluate(LaguerrePolynomial(n), -1) -1: n in [0..40]]; // G. C. Greubel, Aug 11 2022
(SageMath) [factorial(n)*laguerre(n, -1) -1 for n in (0..40)] # G. C. Greubel, Aug 11 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ross La Haye, Sep 20 2004
STATUS
approved