A052803 Expansion of e.g.f. (-1 + sqrt(1 + 4*log(1-x)))/(2*log(1-x)).

1, 1, 5, 44, 566, 9674, 207166, 5343456, 161405016, 5591409720, 218592034584, 9521490534720, 457329182411856, 24014921905589328, 1368772939062117936, 84161443919543331840, 5553011951023694408064, 391360838810043628416384, 29342876851060951124158848

Offset

0,3

Comments

Previous name was: A simple grammar.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..360

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 762

Formula

E.g.f.: (1/2)/log(-1/(-1+x))*(1-(1-4*log(-1/(-1+x)))^(1/2)).

a(n) ~ 2*sqrt(2) * n^(n-1) / (exp(3*n/4) * (exp(1/4)-1)^(n-1/2)). - Vaclav Kotesovec, Sep 30 2013

a(n) = Sum_{k=0..n} (2k)!/(k+1)! * |Stirling1(n,k)|. - Michael D. Weiner, Dec 23 2014

E.g.f.: 1/(1 + log(1-x)/(1 + log(1-x)/(1 + log(1-x)/(1 + log(1-x)/(1 + ...))))), a continued fraction. - Ilya Gutkovskiy, Nov 19 2017

Maple

spec := [S, {C=Cycle(Z), S=Sequence(B), B=Prod(C, S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

CoefficientList[Series[-1/(2*Log[1-x]) * (1-(1+4*Log[1-x])^(1/2)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)

Crossrefs

Cf. A006531, A086662, A087152.

Sequence in context: A243697 A106273 A349836 * A377860 A201923 A222059

Adjacent sequences: A052800 A052801 A052802 * A052804 A052805 A052806

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

New name using e.g.f., Vaclav Kotesovec, Sep 30 2013

Status

approved