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A292619 Convolution of number of overpartitions and Catalan numbers. 0
1, 3, 8, 21, 54, 144, 404, 1195, 3712, 12000, 39994, 136400, 473430, 1665868, 5926476, 21275805, 76964808, 280250088, 1026309908, 3777411342, 13965286180, 51837285776, 193107846304, 721732334136, 2705480787422, 10169387310362, 38320472420462, 144733083435688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

FORMULA

a(n) ~ c * 4^n / (sqrt(Pi) * n^(3/2)), where c = QPochhammer[-1, 1/4] / (2*QPochhammer[1/4, 1/4]) = 1.96926035366826943194719369696726567...

MATHEMATICA

Table[Sum[Sum[PartitionsP[k-j] * PartitionsQ[j], {j, 0, k}] * CatalanNumber[n-k], {k, 0, n}], {n, 0, 50}]

CROSSREFS

Cf. A000108, A015128, A014329, A292617.

Sequence in context: A242452 A190139 A005580 * A231222 A231436 A027932

Adjacent sequences:  A292616 A292617 A292618 * A292620 A292621 A292622

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 20 2017

STATUS

approved

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Last modified November 22 01:14 EST 2019. Contains 329383 sequences. (Running on oeis4.)