OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k) * S(2k,k) * S(2n-2k,n-k).
Limit n->infinity (a(n)/n!)^(1/n) = -4/(LambertW(-2*exp(-2))*(2+LambertW(-2*exp(-2)))) = 6.17655460948348... . - Vaclav Kotesovec, Jun 01 2015
MAPLE
seq(sum(binomial(n, k) *combinat[stirling2](2*k, k) *combinat[stirling2](2*(n-k), n-k), k=0..n), n=0..12);
MATHEMATICA
Table[Sum[Binomial[n, k]StirlingS2[2k, k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 16}]
PROG
(Maxima) makelist(sum(binomial(n, k)*stirling2(2*k, k)*stirling2(2*n-2*k, n-k), k, 0, n), n, 0, 12);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 12 2011
STATUS
approved