OFFSET
0,3
FORMULA
Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} (-2)^n * x^n / n!^3.
MATHEMATICA
Table[Sum[Binomial[n, k]^3 k! (-2)^(n - k), {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[BesselI[0, 2 Sqrt[x]] Sum[(-2)^k x^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)^3 * k! * (-2)^(n-k)); \\ Michel Marcus, Jun 12 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 12 2022
STATUS
approved