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Denominator of the sum of inverse products of parts in all compositions of n.
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%I #12 Feb 12 2024 07:57:59

%S 1,1,2,3,3,60,360,70,1680,3780,75600,138600,285120,129729600,

%T 363242880,3405402000,1009008000,308756448000,5557616064000,

%U 52797352608000,351982350720000,221748880953600,1524523556556000,738190353700800,13464592051502592000

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

%C Denominators of the INVERT transform of reciprocal integers.

%H Alois P. Heinz, <a href="/A323340/b323340.txt">Table of n, a(n) for n = 0..506</a>

%F a(n) = denominator( A007840(n)/n! ).

%p b:= proc(n) option remember;

%p `if`(n=0, 1, add(b(n-j)/j, j=1..n))

%p end:

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

%p seq(a(n), n=0..25);

%t nmax = 20; Denominator[CoefficientList[Series[1/(1 + Log[1-x]), {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Feb 12 2024 *)

%Y See A323339 for more information.

%Y Cf. A000142, A007840.

%K nonn,frac

%O 0,3

%A _Alois P. Heinz_, Jan 11 2019