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A052803 E.g.f.: -1/(2*log(1-x))*(1-(1+4*log(1-x))^(1/2)). 2
1, 1, 5, 44, 566, 9674, 207166, 5343456, 161405016, 5591409720, 218592034584, 9521490534720, 457329182411856, 24014921905589328, 1368772939062117936, 84161443919543331840, 5553011951023694408064, 391360838810043628416384 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Previous name was: A simple grammar.

LINKS

Table of n, a(n) for n=0..17.

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((2k)!/(k+1)! * |stirling1(n,k)|, k=0..n). - Michael D. Weiner, Dec 23 2014

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

Sequence in context: A195242 A243697 A106273 * A201923 A222059 A252931

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

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Last modified December 6 03:18 EST 2016. Contains 278772 sequences.