A307755 Exponential convolution of partition numbers (A000041) with themselves.

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

Vaclav Kotesovec, Table of n, a(n) for n = 0..3000

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

Cf. A000041, A000712, A218481, A307756.

Sequence in context: A324166 A355388 A351787 * A304200 A081057 A000137

Adjacent sequences: A307752 A307753 A307754 * A307756 A307757 A307758

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 26 2019

Status

approved