A353910 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + sinh(x).

1, -2, 1, -28, 21, -146, 1023, -56400, 84745, -975502, 10925883, -57795112, 1994183205, -32047567540, 489891177051, -43944425632000, 158096182329585, -3254060029210454, 64115697136312563, -921897484040044728, 31920276313015362525, -812922524976721463020

Offset: 1

Author

Ilya Gutkovskiy, May 10 2022

Keywords

• sign

Crossrefs

Cf. A353608, A353873, A353911, A353912.

Programs

Mathematica

nn = 22; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Sinh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten