Search: id:A006963
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%I A006963 M3076
%S A006963 1,1,3,20,210,3024,55440,1235520,32432400,980179200,33522128640,1279935820800,
%T A006963 53970627110400,2490952020480000,124903451312640000,6761440164390912000,
%U A006963 393008709555221760000,24412776311194951680000,1613955767240110694400000
%N A006963 Number of planar embedded labeled trees with n nodes: (2n-3)!/(n-1)!.
%D A006963 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006963 P. Leroux and B. Miloudi, ``G\'{e}n\'{e}ralisations de la formule d'Otter,
               '' Ann. Sci. Math. Qu\'{e}bec, Vol. 16, No. 1, pp. 53-80, 1992.
%H A006963 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%H A006963 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=109">
               Encyclopedia of Combinatorial Structures 109</a>
%F A006963 E.g.f. for a(n+1), n >= 1, ln(c(x)); c(x) = g.f. for Catalan numbers 
               A000108 - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
%F A006963 Integral representation as n-th moment of a positive function on a positive 
               half-axis, in Maple notation: a(n)=int(x^n*erfc(sqrt(x)/2)/2, x=0..infinity), 
               n=0, 1..., where erfc(x) is the complementary error function. - Karol 
               A. Penson (penson(AT)lptl.jussieu.fr), Sep 27 2001
%F A006963 a(n) ~ 2^(-5/2)*n^-2*2^(2*n)*e^-n*n^n - Joe Keane (jgk(AT)jgk.org), Jun 
               06 2002
%p A006963 a:=n->mul(j+add(1, j=0..n),j=1..n):seq(a(n), n=-1..18);# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Dec 06 2008]
%p A006963 with(finance):seq(mul(cashflows([n,k,1],0), k=1..n), n=0..22);# [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
%Y A006963 Sequence in context: A052590 A081209 A014068 this_sequence A113333 A052851 
               A058477
%Y A006963 Adjacent sequences: A006960 A006961 A006962 this_sequence A006964 A006965 
               A006966
%K A006963 nonn,easy,nice
%O A006963 1,3
%A A006963 Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).

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