A322365 Denominator of the sum of inverse products of parts in all partitions of n.

1, 1, 2, 6, 3, 10, 180, 1260, 560, 15120, 151200, 26400, 4989600, 4633200, 1528800, 851350500, 54486432000, 34306272000, 793945152000, 105594705216000, 1396755360000, 77534573760000, 243923769048960000, 23087434930560000, 67322960257512960000, 4371620795942400000

Offset: 0

Author

Alois P. Heinz, Dec 04 2018

Keywords

• nonn
• frac

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..506

Crossrefs

See A322364 for more information.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
      b(n, i-1) +b(n-i, min(i, 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 || i==1, 1, b[n, i-1]+b[n-i, Min[i, n-i]]/i];
a[n_] := Denominator[b[n, n]];
a /@ Range[0, 30] (* Jean-François Alcover, Apr 29 2020, after Alois P. Heinz *)

PARI

a(n) = {my(s=0); forpart(p=n, s += 1/vecprod(Vec(p))); denominator(s);} \\ Michel Marcus, Apr 29 2020