A136651 Self-convolution of A014070: a(n) = Sum_{k=0..n} C(2^k,k)*C(2^(n-k),n-k).

1, 4, 16, 136, 3900, 410704, 150779216, 189354108224, 819706419291728, 12417873698752685696, 668556572391910046409088, 129665687275486846550512590336, 91623983383737723477835280780455168, 238057598315149125515904595621291745671168, 2291332225550784443587332334013451028612830795776

Offset: 0

Author

Paul D. Hanna, Jan 16 2008

Keywords

• nonn

Crossrefs

Cf. A014070 (C(2^n, n)).

Programs

Mathematica

Table[Sum[Binomial[2^k,k]*Binomial[2^(n-k),n-k], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)

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),", "))

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