A354277 - OEIS

%I #7 May 23 2022 05:38:45

%S 0,1,2,3,24,70,720,4305,39200,337176,3628800,38417610,479001600,

%T 6128488080,87104969952,1297383162075,20922789888000,354250929192160,

%U 6402373705728000,121407227453840328,2432849766865689600,51041047393559059200,1124000727777607680000

%N Product_{n>=1} 1 / (1 - x^n/n!)^a(n) = exp(-x) / (1 - x).

%F a(1) = 0; a(n) = (n-1)! * (1 - Sum_{d|n, 1 < d < n} d * d!^(-n/d) * a(d)).

%t a[1] = 0; a[n_] := a[n] = (n - 1)! (1 - Sum[d d!^(-n/d) a[d], {d, Divisors[n]~Complement~{1, n}}]); Table[a[n], {n, 1, 23}]

%Y Cf. A000166, A006973, A137852, A353822, A354278.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 22 2022