OFFSET
0,3
COMMENTS
Generally, for p>=1 is Sum_{k=0..n} (k!)^(2*p) * StirlingS2(n,k)^p asymptotic to c * (n!)^(2*p), where c = 1 + Sum_{n>=1} 1/(Product_{k=1..n} (2*k)^p).
FORMULA
a(n) ~ c * (n!)^6, where c = 1.1269621849236767... = 1 + Sum_{n>=1} 1/(Product_{k=1..n} (2*k)^3) = HypergeometricPFQ[{}, {1, 1}, 1/8].
MAPLE
a:= n-> add(k!^6*Stirling2(n, k)^3, k=0..n):
seq(a(n), n=0..15); # Alois P. Heinz, Oct 23 2023
MATHEMATICA
Table[Sum[(k!)^6 * StirlingS2[n, k]^3, {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, May 10 2014
STATUS
approved