OFFSET
0,3
FORMULA
a(n) = n!^3 * [x^n] BesselI(0,2*sqrt(x)) * Sum_{k>=0} (-n)^k * x^k / k!^3.
MATHEMATICA
Unprotect[Power]; 0^0 = 1; Table[Sum[Binomial[n, k]^3 k! (-n)^(n - k), {k, 0, n}], {n, 0, 17}]
Unprotect[Power]; 0^0 = 1; Table[n!^3 SeriesCoefficient[BesselI[0, 2 Sqrt[x]] Sum[(-n)^k x^k/k!^3, {k, 0, n}], {x, 0, n}], {n, 0, 17}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)^3 * k! * (-n)^(n-k)); \\ Michel Marcus, Jun 12 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 12 2022
STATUS
approved