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A292617 Convolution of number of partitions into distinct parts and Catalan numbers. 1
1, 2, 4, 10, 25, 70, 209, 656, 2137, 7155, 24447, 84864, 298374, 1060151, 3800365, 13727145, 49910870, 182522747, 670896855, 2477250003, 9184502747, 34177467134, 127606759053, 477890336663, 1794697782990, 6757164079051, 25501212956975, 96450275088260 (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 = 1.3559096738634793803455442348539593...

MATHEMATICA

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

CROSSREFS

Cf. A000009, A000108, A014329.

Sequence in context: A052829 A001998 A005817 * A148093 A206289 A148094

Adjacent sequences:  A292614 A292615 A292616 * A292618 A292619 A292620

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 20 2017

STATUS

approved

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Last modified February 23 22:58 EST 2018. Contains 299595 sequences. (Running on oeis4.)