A385426 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-arcsin(x)) ).

1, 1, 3, 17, 145, 1665, 24115, 422305, 8681985, 205042625, 5471351875, 162811832625, 5345929731025, 192007183247425, 7488448738333875, 315170338129570625, 14238153926819850625, 687220571240324330625, 35293921478604240911875, 1921751625123502012140625

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f. A(x) satisfies A(x) = exp( arcsin(x*A(x)) ).

a(n) = Sum_{k=0..n} (n+1)^(k-1) * A385343(n,k).

a(n) ~ 2^((n-1)/2) * n^(n-1) / exp((1 - Pi/4)*n - Pi/4). - Vaclav Kotesovec, Feb 01 2026

Mathematica

nmax = 20; CoefficientList[1/x * InverseSeries[Series[x/E^ArcSin[x], {x, 0, nmax + 1}], x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Feb 01 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(-asin(x)))/x))

Crossrefs

Cf. A385424, A385427.

Cf. A001147, A381145, A227464, A385343.

Sequence in context: A015735 A290579 A140983 * A241805 A368233 A277466

Adjacent sequences: A385423 A385424 A385425 * A385427 A385428 A385429

Keyword

nonn

Author

Seiichi Manyama, Jun 28 2025

Status

approved