A356270 a(n) = Sum_{k=0..n} binomial(2*k, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).

1, 3, 9, 49, 189, 945, 4641, 21801, 99021, 487981, 2335541, 10800725, 51363065, 238573865, 1121139065, 5309312105, 24543884585, 113220920945, 530677144745, 2439321389945, 11261499234425, 52169097691865, 239433905462945, 1095710701133345, 5029918350471545

Offset: 0

Author

Vaclav Kotesovec, Aug 01 2022

Keywords

• nonn

Crossrefs

Cf. A000009, A006134, A032443, A266232, A307496, A356268, A356269.

Programs

Mathematica

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

Formula

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

a(n) ~ 2^(2*n) * exp(Pi*sqrt(n/3)) / (3^(5/4) * sqrt(Pi) * n^(5/4)).