A356269 a(n) = Sum_{k=0..n} binomial(2*k, k) * p(k), where p(k) is the partition function A000041.

1, 3, 15, 75, 425, 2189, 12353, 63833, 346973, 1805573, 9565325, 49069517, 257289529, 1307750129, 6723491129, 34024174649, 172873744739, 865954792079, 4359881882579, 21679061144579, 108108834714719, 534409071271199, 2642716232918639, 12975671796056639, 63765647596939139

Offset: 0

Author

Vaclav Kotesovec, Aug 01 2022

Keywords

• nonn

Crossrefs

Cf. A000041, A006134, A032443, A218481, A286955, A356267, A356270.

Programs

Mathematica

Table[Sum[Binomial[2*k, k] * PartitionsP[k], {k, 0, n}], {n, 0, 30}]

Formula

a(n) ~ binomial(2*n,n) * p(n) * 4/3.

a(n) ~ 2^(2*n) * exp(Pi*sqrt(2*n/3)) / (3^(3/2) * sqrt(Pi) * n^(3/2)).