OFFSET
0,2
FORMULA
Recurrence: n*(8*n - 23)*a(n) = 3*(8*n^3 - 15*n^2 - 30*n + 17)*a(n-1) - (n-1)*(24*n^3 - 261*n^2 + 770*n - 666)*a(n-2) + (n-2)^3*(n-1)*(8*n - 15)*a(n-3).
a(n) ~ n^(n - 1/6) * exp(3*3^(1/3)*n^(2/3) - 3^(2/3)*n^(1/3) - n +1) / (3^(5/6)*sqrt(2*Pi)) * (1 + 19/(6*3^(2/3)*n^(1/3)) + 1193/(1080*3^(1/3) * n^(2/3))).
Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} 3^n * x^n / n!^3. - Ilya Gutkovskiy, Jun 19 2022
MATHEMATICA
Table[Sum[Binomial[n, k]^3 * 3^(n-k) * k!, {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 12 2016
STATUS
approved