A322365 - OEIS

%I #15 Apr 29 2020 10:02:03

%S 1,1,2,6,3,10,180,1260,560,15120,151200,26400,4989600,4633200,1528800,

%T 851350500,54486432000,34306272000,793945152000,105594705216000,

%U 1396755360000,77534573760000,243923769048960000,23087434930560000,67322960257512960000,4371620795942400000

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

%H Alois P. Heinz, <a href="/A322365/b322365.txt">Table of n, a(n) for n = 0..506</a>

%p b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,

%p       b(n, i-1) +b(n-i, min(i, n-i))/i)

%p     end:

%p a:= n-> denom(b(n$2)):

%p seq(a(n), n=0..30);

%t b[n_, i_] := b[n, i] = If[n==0 || i==1, 1, b[n, i-1]+b[n-i, Min[i, n-i]]/i];

%t a[n_] := Denominator[b[n, n]];

%t a /@ Range[0, 30] (* _Jean-François Alcover_, Apr 29 2020, after _Alois P. Heinz_ *)

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

%Y See A322364 for more information.

%K nonn,frac

%O 0,3

%A _Alois P. Heinz_, Dec 04 2018