A304823 Convolution of number of partitions into distinct parts and central binomial coefficients.

1, 3, 9, 30, 102, 361, 1308, 4819, 17970, 67614, 256156, 975742, 3733255, 14336290, 55224880, 213298817, 825741010, 3203142338, 12447523904, 48448301960, 188838707898, 736985826174, 2879588370517, 11263139964066, 44096779183060, 172797721166402

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) ~ QPochhammer[-1, 1/4] * 2^(2*n-1) / sqrt(Pi*n).

Mathematica

Table[Sum[PartitionsQ[n-k]*Binomial[2*k, k], {k, 0, n}], {n, 0, 25}]

Crossrefs

Cf. A000009, A000984, A292617, A304824.

Sequence in context: A228339 A257641 A048119 * A317875 A056333 A148948

Adjacent sequences: A304820 A304821 A304822 * A304824 A304825 A304826

Keyword

nonn

Author

Vaclav Kotesovec, May 19 2018

Status

approved