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

Author

Vladimir Joseph Stephan Orlovsky, Dec 13 2008

Keywords

• nonn

Links

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

Crossrefs

Cf. A000009, A000041, A058694.

Programs

Mathematica

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

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

Extensions

Offset corrected by Vaclav Kotesovec, Nov 29 2015