A352404 - OEIS

%I #20 May 15 2022 12:14:32

%S 1,-1,5,-35,204,-1294,16862,-225266,2346712,-31689336,558727872,

%T -9891952608,185546362416,-3668674300992,83728926109488,

%U -2078005263610704,50908186083448320,-1343594571773137536,38998680958184088960,-1181298578244977897856,37029733866954589964544

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

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

%t 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}]

%Y Cf. A157159, A157164, A348205, A348206, A352664, A352691, A352953.

%K sign

%O 1,3

%A _Ilya Gutkovskiy_, May 15 2022