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

%I A322365 #15 Apr 29 2020 10:02:03
%S A322365 1,1,2,6,3,10,180,1260,560,15120,151200,26400,4989600,4633200,1528800,
%T A322365 851350500,54486432000,34306272000,793945152000,105594705216000,
%U A322365 1396755360000,77534573760000,243923769048960000,23087434930560000,67322960257512960000,4371620795942400000
%N A322365 Denominator of the sum of inverse products of parts in all partitions of n.
%H A322365 Alois P. Heinz, <a href="/A322365/b322365.txt">Table of n, a(n) for n = 0..506</a>
%p A322365 b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
%p A322365       b(n, i-1) +b(n-i, min(i, n-i))/i)
%p A322365     end:
%p A322365 a:= n-> denom(b(n$2)):
%p A322365 seq(a(n), n=0..30);
%t A322365 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 A322365 a[n_] := Denominator[b[n, n]];
%t A322365 a /@ Range[0, 30] (* _Jean-François Alcover_, Apr 29 2020, after _Alois P. Heinz_ *)
%o A322365 (PARI) a(n) = {my(s=0); forpart(p=n, s += 1/vecprod(Vec(p))); denominator(s);} \\ _Michel Marcus_, Apr 29 2020
%Y A322365 See A322364 for more information.
%K A322365 nonn,frac
%O A322365 0,3
%A A322365 _Alois P. Heinz_, Dec 04 2018