login
A097662
a(n) = A002720(n) - 1.
3
0, 1, 6, 33, 208, 1545, 13326, 130921, 1441728, 17572113, 234662230, 3405357681, 53334454416, 896324308633, 16083557845278, 306827170866105, 6199668952527616, 132240988644215841, 2968971263911288998, 69974827707903049153, 1727194482044146637520, 44552237162692939114281
OFFSET
0,3
LINKS
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
Main diagonal of A329655.
Sequence in context: A093964 A361776 A193665 * A366200 A277485 A012522
KEYWORD
nonn
AUTHOR
Ross La Haye, Sep 20 2004
STATUS
approved