A152827 Partial products of PartitionsQ numbers (A000009).

1, 1, 1, 2, 4, 12, 48, 240, 1440, 11520, 115200, 1382400, 20736000, 373248000, 8211456000, 221709312000, 7094697984000, 269598523392000, 12401532076032000, 669682732105728000, 42859694854766592000

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..190

Formula

log(a(n)) ~ 2*Pi*n^(3/2)/(3*sqrt(3)) * (1 - 9*sqrt(3)*log(n)/(8*Pi*sqrt(n)) + 3*sqrt(3)*(3 - 8*log(2) - log(3))/(8*Pi*sqrt(n)) + (13/16 - 27/(8*Pi^2))/n). - Vaclav Kotesovec, Nov 30 2015

Mathematica

Table[Product[PartitionsQ[k], {k, 0, n}], {n, 0, 33}]
FoldList[Times, 1, PartitionsQ[Range[20]]] (* Harvey P. Dale, Sep 16 2011 *)

Crossrefs

Cf. A000009, A000041, A058694.

Sequence in context: A321009 A052849 A098558 * A030813 A126772 A030949

Adjacent sequences: A152824 A152825 A152826 * A152828 A152829 A152830

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 13 2008

Extensions

Offset corrected by Vaclav Kotesovec, Nov 29 2015

Status

approved