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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).
3
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
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}]
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 01 2022
STATUS
approved