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

0,3

Links

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

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 *)

Prog

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

Crossrefs

See A322364 for more information.

Sequence in context: A130684 A295644 A079178 * A297553 A347558 A317490

Adjacent sequences: A322362 A322363 A322364 * A322366 A322367 A322368

Keyword

nonn,frac

Author

Alois P. Heinz, Dec 04 2018

Status

approved