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A307755
Exponential convolution of partition numbers (A000041) with themselves.
3
1, 2, 6, 18, 58, 184, 586, 1822, 5618, 16980, 50892, 150064, 439210, 1268924, 3640342, 10337596, 29160638, 81570368, 226795202, 626070664, 1718783084, 4689582366, 12730998988, 34373603158, 92385339242, 247099560046, 658137847408, 1745322097886, 4610549234836, 12131656526628
OFFSET
0,2
LINKS
FORMULA
E.g.f.: (Sum_{k>=0} A000041(k)*x^k/k!)^2.
a(n) = Sum_{k=0..n} binomial(n,k)*A000041(k)*A000041(n-k).
a(n) ~ exp(2*Pi*sqrt(n/3)) * 2^(n-2) / (3*n^2). - Vaclav Kotesovec, May 06 2019
MAPLE
a:= n-> (p-> add(binomial(n, j)*p(j)*p(n-j), j=0..n))(combinat[numbpart]):
seq(a(n), n=0..30); # Alois P. Heinz, Apr 26 2019
MATHEMATICA
nmax = 29; CoefficientList[Series[Sum[PartitionsP[k] x^k/k!, {k, 0, nmax}]^2, {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] PartitionsP[k] PartitionsP[n - k], {k, 0, n}], {n, 0, 29}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 26 2019
STATUS
approved