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A087152 Expansion of (1-sqrt(1-4*log(1+x)))/log(1+x)/2. 1
1, 3, 20, 194, 2554, 42226, 843744, 19769256, 531768120, 16152296424, 546895099200, 20425461026736, 834215500905552, 36988602430554576, 1769524998544143360, 90851799797294235264, 4982968503277896871296 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..370

FORMULA

a(n) = Sum_{k=0..n} Stirling1(n, k)*k!*Catalan(k).

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

MATHEMATICA

Rest[CoefficientList[Series[(1-Sqrt[1-4*Log[1+x]])/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)))/log(1+x)/2 - 1)) \\ G. C. Greubel, May 24 2017

CROSSREFS

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

Sequence in context: A176043 A108206 A120485 * A158833 A296715 A054361

Adjacent sequences:  A087149 A087150 A087151 * A087153 A087154 A087155

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 18 2003

STATUS

approved

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Last modified October 16 11:25 EDT 2018. Contains 316263 sequences. (Running on oeis4.)