OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
G.f.: A(x) = (1/(1+x))*Sum_{n>=0} [log(1 + (2^n+1)*x) - log(1+x)]^n / n!.
a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016
MATHEMATICA
Table[Sum[(-1)^(n-k)*Binomial[n, k]*Binomial[2^k, k], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(PARI) {a(n)=sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(2^k, k))}
(PARI) /* Using the g.f.: */ {a(n)=my(X=x+x*O(x^n)); polcoeff(sum(k=0, n, (log(1+(2^k+1)*X)-log(1+X))^k/k!)/(1+X), n)}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul D. Hanna and Vladeta Jovovic, Jan 21 2008
EXTENSIONS
Edited by Charles R Greathouse IV, Oct 28 2009
Terms a(13) and beyond from Andrew Howroyd, Feb 02 2020
STATUS
approved