A353913 - OEIS

A353913

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

1, -2, 1, -28, 29, -194, 1583, -61328, 144153, -1697262, 20127867, -191762088, 3978820221, -66586416948, 1057400360235, -58260102945024, 370244721585681, -7992573879248406, 162968423791332339, -3399970067764816824, 88052648301403014789, -2360852841450177138924

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

MATHEMATICA

nn = 22; f[x_] := Product[1/(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, A353818, A353873, A353914, A353915.

Sequence in context: A336911 A322230 A353910 * A012411 A012415 A012660

Adjacent sequences: A353910 A353911 A353912 * A353914 A353915 A353916

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, May 10 2022

STATUS

approved