A322381 Denominator of the sum of inverse products of parts in all strict partitions of n.

1, 1, 2, 6, 12, 60, 120, 280, 168, 210, 1680, 2640, 332640, 4324320, 8648640, 43243200, 900900, 735134400, 3150576, 2618916300, 83805321600, 586637251200, 586637251200, 749592043200, 2248776129600, 642507465600, 13492656777600, 41644002400, 53970627110400

Offset: 0

Author

Alois P. Heinz, Dec 05 2018

Keywords

• nonn
• frac

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1268
• Andreas B. G. Blobel, An Asymptotic Form of the Generating Function Prod_{k=1,oo} (1+x^k/k), arXiv:1904.07808 [math.CO], 2019.

Crossrefs

See A322380 for more information.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1) +b(n-i, min(i-1, n-i))/i))
    end:
a:= n-> denom(b(n$2)):
seq(a(n), n=0..30);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + b[n - i, Min[i - 1, n - i]]/i]];
a[n_] := Denominator[b[n, n]];
a /@ Range[0, 30] (* Jean-François Alcover, Feb 25 2020, after Alois P. Heinz *)