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Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + log(1 + x).
6

%I #6 Oct 08 2021 03:46:35

%S 1,-3,5,-68,204,-1394,16862,-413776,2377512,-35594832,558727872,

%T -8067263280,185546362416,-4108304962176,82441247589360,

%U -3519099528152064,50908186083448320,-1465023121035418368,38998680958184088960,-1219845314470474404864,36452994894649858339584

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

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

%Y Cf. A006973, A137852, A157159, A157164, A348206, A348207.

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, Oct 06 2021