A353607 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + sin(x).

1, 0, -1, 4, -19, 114, -659, 5328, -38375, 400430, -3578279, 44920360, -476298835, 6949878740, -85215100151, 1492480745728, -20903398375855, 382829285287446, -6399968826052559, 136747967762351544, -2394435177245209195, 55602194767215266060, -1123931378903214542099

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• sign

Crossrefs

Cf. A006973, A137852, A170914, A170915, A353608, A353609, A353610, A353611.

Programs

Mathematica

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