OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
Recurrence: (8*n^2+31*n+21)*a(n+3) - (24*n^3+157*n^2+308*n+162)*a(n+2) + (24*n^4+117*n^3+178*n^2+71*n-18)*a(n+1) - (8*n^2+31*n+30)*(n+1)^3*a(n) = 0.
a(n) ~ n^(n-1/6)/(sqrt(6*Pi)*exp(n+n^(1/3)-3*n^(2/3)-1/3)). - Vaclav Kotesovec, Sep 30 2012
a(n) = hypergeom([-n, -n, -n], [1], -1). - Vladimir Reshetnikov, Sep 28 2016
a(n) = Sum_{k=0..n} binomial(n, k)*|A021009(n, k)|. - Peter Luschny, May 04 2021
Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} x^n / n!^3. - Ilya Gutkovskiy, Jun 19 2022
MATHEMATICA
Table[Sum[Binomial[n, k]^3*k!, {k, 0, n}], {n, 0, 25}]
Table[HypergeometricPFQ[{-n, -n, -n}, {1}, -1], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 28 2016 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)^3 * k!); \\ Michel Marcus, May 04 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 17 2012
STATUS
approved