A352404 Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + log(1 + x).

1, -1, 5, -35, 204, -1294, 16862, -225266, 2346712, -31689336, 558727872, -9891952608, 185546362416, -3668674300992, 83728926109488, -2078005263610704, 50908186083448320, -1343594571773137536, 38998680958184088960, -1181298578244977897856, 37029733866954589964544

Offset: 1

Author

Ilya Gutkovskiy, May 15 2022

Keywords

• sign

Crossrefs

Cf. A157159, A157164, A348205, A348206, A352664, 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 + 1)/n - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 21}]

Formula

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