A353818 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + arcsin(x).

1, 0, 1, -4, 29, -174, 1583, -13168, 144153, -1485330, 20127867, -253341144, 3978820221, -57986205900, 1057400360235, -18016221644544, 370244721585681, -6993826454599146, 162968423791332339, -3490951922268853320, 88052648301403014789, -2075060448716599488276

Offset: 1

Author

Ilya Gutkovskiy, May 08 2022

Keywords

• sign

Crossrefs

Cf. A001818, A006973, A137852, A353607, A353819, A353820, A353821.

Programs

Mathematica

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