The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136651 Self-convolution of A014070: a(n) = Sum_{k=0..n} C(2^k,k)*C(2^(n-k),n-k). 0

%I #9 Jul 02 2016 08:00:16

%S 1,4,16,136,3900,410704,150779216,189354108224,819706419291728,

%T 12417873698752685696,668556572391910046409088,

%U 129665687275486846550512590336,91623983383737723477835280780455168,238057598315149125515904595621291745671168,2291332225550784443587332334013451028612830795776

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

%F 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 a(n) ~ 2^(n^2+1) / n!. - _Vaclav Kotesovec_, Jul 02 2016

%t Table[Sum[Binomial[2^k,k]*Binomial[2^(n-k),n-k], {k, 0, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Jul 02 2016 *)

%o (PARI) {a(n) = sum(k=0,n, binomial(2^k,k) * binomial(2^(n-k),n-k) )}

%o for(n=0,20, print1(a(n),", "))

%o (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 for(n=0,20, print1(a(n),", "))

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 16 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 03:48 EST 2023. Contains 367567 sequences. (Running on oeis4.)