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A307945
Exponential convolution of A015128 with themselves.
1
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
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 07 2019
STATUS
approved