|
%I #23 Feb 12 2024 07:57:53
%S 1,1,3,7,11,347,3289,1011,38371,136553,4320019,12528587,40771123,
%T 29346499543,129990006917,1927874590951,903657004321,437445829053473,
%U 12456509813711881,187206004658210129,1974369484466728177,1967745662306280217,21401375717067880189
%N Numerator of the sum of inverse products of parts in all compositions of n.
%C Numerators of the INVERT transform of reciprocal integers.
%H Alois P. Heinz, <a href="/A323339/b323339.txt">Table of n, a(n) for n = 0..466</a>
%F G.f. for fractions: 1 / (1 + log(1 - x)). - _Ilya Gutkovskiy_, Nov 12 2019
%F a(n) = numerator( A007840(n)/n! ). - _Alois P. Heinz_, Jan 04 2024
%F A323339(n)/A323340(n) ~ exp(n) / (exp(1) - 1)^(n+1). - _Vaclav Kotesovec_, Feb 12 2024
%e 1/1, 1/1, 3/2, 7/3, 11/3, 347/60, 3289/360, 1011/70, 38371/1680, 136553/3780, 4320019/75600, 12528587/138600, 40771123/285120, ... = A323339/A323340
%p b:= proc(n) option remember;
%p `if`(n=0, 1, add(b(n-j)/j, j=1..n))
%p end:
%p a:= n-> numer(b(n)):
%p seq(a(n), n=0..25);
%t nmax = 20; Numerator[CoefficientList[Series[1/(1 + Log[1-x]), {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Feb 12 2024 *)
%Y Denominators: A323340.
%Y Cf. A000142, A007840, A011782, A088305, A177208, A177209, A322364, A322365, A322380, A322381, A323290, A323291.
%K nonn,frac
%O 0,3
%A _Alois P. Heinz_, Jan 11 2019
|
