A356270 - OEIS

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

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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.