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

0,2

Links

Table of n, a(n) for n=0..24.

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)).

Mathematica

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

Crossrefs

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

Sequence in context: A141051 A001530 A316449 * A190009 A012063 A036751

Adjacent sequences: A356267 A356268 A356269 * A356271 A356272 A356273

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved