|
|
|
|
0, 1, 6, 33, 208, 1545, 13326, 130921, 1441728, 17572113, 234662230, 3405357681, 53334454416, 896324308633, 16083557845278, 306827170866105, 6199668952527616, 132240988644215841, 2968971263911288998, 69974827707903049153, 1727194482044146637520, 44552237162692939114281
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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.
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:
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|