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

1,4

Links

Table of n, a(n) for n=1..22.

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

Crossrefs

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

Sequence in context: A300806 A303464 A301445 * A198794 A258416 A079885

Adjacent sequences: A353815 A353816 A353817 * A353819 A353820 A353821

Keyword

sign

Author

Ilya Gutkovskiy, May 08 2022

Status

approved