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Expansion of e.g.f.: 1/Product_{m>0} (1-x^m/(m-1)!).
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%I #16 Nov 04 2020 06:52:05

%S 1,1,4,15,88,505,4056,31549,311816,3083049,36343720,431215741,

%T 5937234348,82236865165,1291252453050,20477737537755,361495828272496,

%U 6449450737736065,126566562342343176,2509520619696338269,54179963857121953460,1182248224137860933781

%N Expansion of e.g.f.: 1/Product_{m>0} (1-x^m/(m-1)!).

%H Alois P. Heinz, <a href="/A076900/b076900.txt">Table of n, a(n) for n = 0..450</a>

%F E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*((j - 1)!)^k)). - _Ilya Gutkovskiy_, Sep 13 2018

%F a(n) ~ c * n * n!, where c = A247551/2. - _Vaclav Kotesovec_, Sep 13 2018

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

%p b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(n, i)*i)))

%p end:

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

%p seq(a(n), n=0..30); # _Alois P. Heinz_, May 11 2016

%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i-1] + If[i > n, 0, b[n-i, i] Binomial[n, i] i]]];

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

%t a /@ Range[0, 30] (* _Jean-François Alcover_, Nov 03 2020, after _Alois P. Heinz_ *)

%Y Cf. A005651, A032299.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Nov 26 2002