OFFSET
0,2
FORMULA
a(n) = sum((-1)^(n-k)*c(k)^2,k=0..n), where c(n) = A080253(n).
a(n) ~ (n!)^2 * 2^(2*n-1) / (log(2))^(2*n + 2). - Vaclav Kotesovec, Nov 27 2017
MATHEMATICA
t[n_] := Sum[StirlingS2[n, k] k!, {k, 0, n}]; c[n_] := Sum[Binomial[n, k] 2^k t[k], {k, 0, n}]; Table[Sum[(-1)^(n-k)c[k]^2, {k, 0, n}], {n, 0, 100}]
PROG
(Maxima) t(n):=sum(stirling2(n, k)*k!, k, 0, n);
c(n):=sum(binomial(n, k)*2^k*t(k), k, 0, n);
makelist(sum((-1)^(n-k)*c(k)^2, k, 0, n), n, 0, 40);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Oct 04 2012
STATUS
approved