A087138 Expansion of (1-sqrt(1-4*log(1+x)))/2.

1, 1, 8, 64, 824, 12968, 252720, 5789712, 153169440, 4589004192, 153643615872, 5684390364288, 230307823878144, 10141452865049088, 482259966649655808, 24630247225278881280, 1344614199041549399040, 78137673004382654223360

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..372

Index entries for reversions of series

Formula

a(n) = Sum_{k=1..n} Stirling1(n, k)*k!*Catalan(k-1).

a(n) ~ n! / (2*exp(1/8)*sqrt(Pi) * (exp(1/4)-1)^(n-1/2) * n^(3/2)). - Vaclav Kotesovec, May 03 2015

From Seiichi Manyama, Sep 09 2024: (Start)

E.g.f. satisfies A(x) = (log(1 + x)) / (1 - A(x)).

E.g.f.: Series_Reversion( exp(x * (1 - x)) - 1 ). (End)

Mathematica

Rest[CoefficientList[Series[(1-Sqrt[1-4*Log[1+x]])/2, {x, 0, 20}], x] * Range[0, 20]!] (* Vaclav Kotesovec, May 03 2015 *)

Prog

(PARI) x='x+O('x^50); Vec(serlaplace((1-sqrt(1-4*log(1+x)))/2)) \\ G. C. Greubel, May 24 2017

Crossrefs

Cf. A000108, A052851, A052803, A052886, A052895, A006531, A048287, A293604.

Cf. A370462, A370463.

Sequence in context: A133054 A371988 A098560 * A293144 A349266 A111984

Adjacent sequences: A087135 A087136 A087137 * A087139 A087140 A087141

Keyword

nonn,changed

Author

Vladeta Jovovic, Oct 18 2003

Status

approved