OFFSET
0,3
COMMENTS
Generally, for p>=1 is Sum_{k=0..n} (k!*StirlingS2(n,k))^p asymptotic to n^(p*n+1/2) * sqrt(Pi/(2*p*(1-log(2))^(p-1))) / (exp(p*n) * log(2)^(p*n+1)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..169
FORMULA
a(n) ~ sqrt(Pi/6) * n^(3*n+1/2) / ((1-log(2)) * exp(3*n) * (log(2))^(3*n+1)).
MATHEMATICA
Table[Sum[(k!)^3 * StirlingS2[n, k]^3, {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, May 10 2014
STATUS
approved