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%I #10 May 08 2022 08:45:04
%S 1,0,-1,4,-19,114,-659,5328,-38375,400430,-3578279,44920360,
%T -476298835,6949878740,-85215100151,1492480745728,-20903398375855,
%U 382829285287446,-6399968826052559,136747967762351544,-2394435177245209195,55602194767215266060,-1123931378903214542099
%N Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + sin(x).
%t nn = 23; f[x_] := Product[(1 + a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Sin[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y Cf. A006973, A137852, A170914, A170915, A353608, A353609, A353610, A353611.
%K sign
%O 1,4
%A _Ilya Gutkovskiy_, May 07 2022