OFFSET
0,2
FORMULA
G.f.: A(x) = Sum_{n>=0} (1/n!)*Sum_{k=0..n} C(n,k) * log(1+2^k*x)^k * log(1+2^(n-k)*x)^(n-k).
a(n) ~ 2^(n^2+1) / n!. - Vaclav Kotesovec, Jul 02 2016
MATHEMATICA
Table[Sum[Binomial[2^k, k]*Binomial[2^(n-k), n-k], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(2^k, k) * binomial(2^(n-k), n-k) )}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n) = polcoeff( sum(m=0, n, sum(k=0, m, log(1+2^k*x +x*O(x^n))^k/k! * log(1+2^(m-k)*x +x*O(x^n))^(m-k) / (m-k)! ) ), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 16 2008
STATUS
approved