A352664 Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 - log(1 - x).

1, 1, -1, 13, -16, -34, -526, 22142, -10424, -160536, -2805408, -29182944, -374664720, -3220913760, 32949033168, 11465880121776, -16610113920768, -96543735968640, -5110200130727808, -130871898552663936, 1042965176555775744, -29461082210774712576

Offset: 1

Author

Ilya Gutkovskiy, May 15 2022

Keywords

• sign

Crossrefs

Cf. A157159, A157164, A348205, A348206, A352404, A352691, A352953.

Programs

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[c[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; c[n_] := c[n] = 1/n - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 22}]

Formula

Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + Sum_{n>=1} x^n/n.