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A352404
Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + log(1 + x).
3
1, -1, 5, -35, 204, -1294, 16862, -225266, 2346712, -31689336, 558727872, -9891952608, 185546362416, -3668674300992, 83728926109488, -2078005263610704, 50908186083448320, -1343594571773137536, 38998680958184088960, -1181298578244977897856, 37029733866954589964544
OFFSET
1,3
FORMULA
Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 - Sum_{n>=1} (-x)^n/n.
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}]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 15 2022
STATUS
approved