A307945 Exponential convolution of A015128 with themselves.

1, 4, 16, 64, 252, 968, 3616, 13120, 46432, 160772, 545856, 1821056, 5979520, 19350552, 61795968, 194964672, 608261628, 1878140024, 5743681784, 17408223328, 52320105080, 156011658272, 461763417056, 1357182242560, 3962591708576, 11497241014652

Offset: 0

Author

Vaclav Kotesovec, May 07 2019

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..2994

Crossrefs

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

Programs

Maple

S:= series(1/JacobiTheta4(0,q),q,101):
f:= n -> add(binomial(n,k)*coeff(S,q,k)*coeff(S,q,n-k),k=0..n):
map(f, [$0..100]); # Robert Israel, May 08 2019

Mathematica

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}]

Formula

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

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