A353608 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + sinh(x).

1, 0, 1, -4, 21, -126, 1023, -8240, 84745, -864370, 10925883, -133566808, 1994183205, -28455880012, 489891177051, -8112780640000, 158096182329585, -2911196026492074, 64115697136312563, -1328879415116924744, 31920276313015362525, -728711636884140292372

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• sign

Crossrefs

Cf. A006973, A137852, A353607, A353609, A353610, A353611.

Programs

Mathematica

nn = 22; f[x_] := Product[(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