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A052851 E.g.f.: 1/2 - 1/2*(1+4*log(1-x))^(1/2). 2
0, 1, 3, 20, 220, 3424, 69008, 1706256, 49956240, 1689497376, 64799254752, 2778906776832, 131756614920192, 6843405231815424, 386414606189283072, 23567401521343170048, 1543994621969805135360, 108137637714495023354880, 8062825821198926369725440 (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..18.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 819

FORMULA

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

a(n) = Sum_{k=1..n} stirling1(n,k)*k!*C(2*k-2,k-1)/k*(-1)^(n+k). - Vladimir Kruchinin, May 12 2012

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

MAPLE

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

MATHEMATICA

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

PROG

(Maxima) a(n):=sum(stirling1(n, k)*k!*binomial(2*k-2, k-1)/k*(-1)^(n+k), k, 1, n); \\ Vladimir Kruchinin, May 12 2012

CROSSREFS

Sequence in context: A113333 A206405 A307363 * A262233 A058477 A119758

Adjacent sequences:  A052848 A052849 A052850 * A052852 A052853 A052854

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 November 25 13:47 EST 2020. Contains 338623 sequences. (Running on oeis4.)