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

%I A322381 #13 Feb 25 2020 08:14:40
%S A322381 1,1,2,6,12,60,120,280,168,210,1680,2640,332640,4324320,8648640,
%T A322381 43243200,900900,735134400,3150576,2618916300,83805321600,
%U A322381 586637251200,586637251200,749592043200,2248776129600,642507465600,13492656777600,41644002400,53970627110400
%N A322381 Denominator of the sum of inverse products of parts in all strict partitions of n.
%H A322381 Alois P. Heinz, <a href="/A322381/b322381.txt">Table of n, a(n) for n = 0..1268</a>
%H A322381 Andreas B. G. Blobel, <a href="https://arxiv.org/abs/1904.07808">An Asymptotic Form of the Generating Function Prod_{k=1,oo} (1+x^k/k)</a>, arXiv:1904.07808 [math.CO], 2019.
%p A322381 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A322381       b(n, i-1) +b(n-i, min(i-1, n-i))/i))
%p A322381     end:
%p A322381 a:= n-> denom(b(n$2)):
%p A322381 seq(a(n), n=0..30);
%t A322381 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]];
%t A322381 a[n_] := Denominator[b[n, n]];
%t A322381 a /@ Range[0, 30] (* _Jean-François Alcover_, Feb 25 2020, after _Alois P. Heinz_ *)
%Y A322381 See A322380 for more information.
%K A322381 nonn,frac
%O A322381 0,3
%A A322381 _Alois P. Heinz_, Dec 05 2018