login
Exponential convolution of A015128 with themselves.
1

%I #8 May 08 2019 23:11:15

%S 1,4,16,64,252,968,3616,13120,46432,160772,545856,1821056,5979520,

%T 19350552,61795968,194964672,608261628,1878140024,5743681784,

%U 17408223328,52320105080,156011658272,461763417056,1357182242560,3962591708576,11497241014652

%N Exponential convolution of A015128 with themselves.

%H Robert Israel, <a href="/A307945/b307945.txt">Table of n, a(n) for n = 0..2994</a>

%F a(n) = Sum_{k=0..n} binomial(n,k) * A015128(k) * A015128(n-k).

%F a(n) ~ 2^(n-4) * exp(Pi*sqrt(2*n)) / n^2.

%p S:= series(1/JacobiTheta4(0,q),q,101):

%p f:= n -> add(binomial(n,k)*coeff(S,q,k)*coeff(S,q,n-k),k=0..n):

%p map(f, [$0..100]); # _Robert Israel_, May 08 2019

%t A015128[n_]:=Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}]; Table[Sum[Binomial[n, k]*A015128[k]*A015128[n-k], {k, 0, n}], {n, 0, 25}]

%Y Cf. A015128, A266497, A294499, A307755, A307756.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, May 07 2019