A354277 Product_{n>=1} 1 / (1 - x^n/n!)^a(n) = exp(-x) / (1 - x).
0, 1, 2, 3, 24, 70, 720, 4305, 39200, 337176, 3628800, 38417610, 479001600, 6128488080, 87104969952, 1297383162075, 20922789888000, 354250929192160, 6402373705728000, 121407227453840328, 2432849766865689600, 51041047393559059200, 1124000727777607680000
Offset: 1
Keywords
Programs
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Mathematica
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}]
Formula
a(1) = 0; a(n) = (n-1)! * (1 - Sum_{d|n, 1 < d < n} d * d!^(-n/d) * a(d)).