A097662 a(n) = A002720(n) - 1.

0, 1, 6, 33, 208, 1545, 13326, 130921, 1441728, 17572113, 234662230, 3405357681, 53334454416, 896324308633, 16083557845278, 306827170866105, 6199668952527616, 132240988644215841, 2968971263911288998, 69974827707903049153, 1727194482044146637520, 44552237162692939114281

Offset: 0

Author

Ross La Haye, Sep 20 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A002720, A008279, A129833.

Main diagonal of A329655.

Programs

Magma

[Factorial(n)*Evaluate(LaguerrePolynomial(n), -1) -1: n in [0..40]]; // G. C. Greubel, Aug 11 2022

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 *)

SageMath

[factorial(n)*laguerre(n, -1) -1 for n in (0..40)] # G. C. Greubel, Aug 11 2022

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)