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

0,2

Links

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

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.

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}]

Crossrefs

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

Sequence in context: A267975 A269489 A259898 * A370143 A269771 A228980

Adjacent sequences: A307942 A307943 A307944 * A307946 A307947 A307948

Keyword

nonn

Author

Vaclav Kotesovec, May 07 2019

Status

approved