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A014329 Convolution of partition numbers and Catalan numbers. 6
1, 2, 5, 12, 31, 84, 245, 752, 2413, 7991, 27104, 93605, 327886, 1161735, 4155323, 14982399, 54393829, 198666117, 729443563, 2690890444, 9968312790, 37066929338, 138304185107, 517646986719, 1942966098461, 7311862919106, 27582428518833, 104279585166245 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ c * 4^n / (sqrt(Pi) * n^(3/2)), where c = Sum_{k>=0} A000041(k)/4^k = 1/QPochhammer[1/4, 1/4] = 1.4523536424495970158347130224852748733612279788... . - Vaclav Kotesovec, Jun 23 2015

MATHEMATICA

Table[Sum[PartitionsP[k]*CatalanNumber[n-k], {k, 0, n}], {n, 0, 50}] (* Vaclav Kotesovec, Jun 23 2015 *)

CROSSREFS

Cf. A000041, A000108, A292617.

Sequence in context: A271929 A071359 A160999 * A045633 A090826 A132441

Adjacent sequences:  A014326 A014327 A014328 * A014330 A014331 A014332

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 12 11:25 EDT 2020. Contains 335658 sequences. (Running on oeis4.)