cp's OEIS Frontend

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

%I A136651 #9 Jul 02 2016 08:00:16
%S A136651 1,4,16,136,3900,410704,150779216,189354108224,819706419291728,
%T A136651 12417873698752685696,668556572391910046409088,
%U A136651 129665687275486846550512590336,91623983383737723477835280780455168,238057598315149125515904595621291745671168,2291332225550784443587332334013451028612830795776
%N A136651 Self-convolution of A014070: a(n) = Sum_{k=0..n} C(2^k,k)*C(2^(n-k),n-k).
%F A136651 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).
%F A136651 a(n) ~ 2^(n^2+1) / n!. - _Vaclav Kotesovec_, Jul 02 2016
%t A136651 Table[Sum[Binomial[2^k,k]*Binomial[2^(n-k),n-k], {k, 0, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Jul 02 2016 *)
%o A136651 (PARI) {a(n) = sum(k=0,n, binomial(2^k,k) * binomial(2^(n-k),n-k) )}
%o A136651 for(n=0,20, print1(a(n),", "))
%o A136651 (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)}
%o A136651 for(n=0,20, print1(a(n),", "))
%Y A136651 Cf. A014070 (C(2^n, n)).
%K A136651 nonn
%O A136651 0,2
%A A136651 _Paul D. Hanna_, Jan 16 2008