Search: id:A058987
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%I A058987
%S A058987 0,1,3,10,33,111,378,1303,4539,15961,56598,202214,727389,2632605,
%T A058987 9581211,35047098,128791323,475281921,1760726808,6545921136,24415415001,
%U A058987 91340016081,342658850427,1288774386909,4858753673655,18358309669651
%N A058987 Catalan(n) - Motzkin(n-1).
%C A058987 Number of Dyck paths with a "small Capital N" (a rise then a fall then 
               a rise) - this follows from the exercise on p. 238 of Stanley stating 
               that Motzkin numbers equal to the ballot number without (1,-1,1). 
               Since Ballot numbers are Catalan numbers, the result follows from 
               the well-known bijection with Dyck paths.
%C A058987 a(n+1)=p(n+1) where p(x) is the unique degree-n polynomial such that 
               p(k)=Catalan(k+1) for k=0,1,...,n. - Michael Somos, Oct 07 2003
%D A058987 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; cf. 
               p. 238.
%H A058987 Harry J. Smith, <a href="b058987.txt">Table of n, a(n) for n=1,...,100</
               a>
%o A058987 (PARI) a(n)=if(n<1,0,subst(polinterpolate(vector(n,k,binomial(2*k,k)/
               (k+1))),x,n+1))
%o A058987 (PARI) { allocatemem(932245000); for (n = 1, 100, a=if(n<=1, 0, subst(polinterpolate(vector(n-1,
               k,binomial(2*k,k)/(k+1))),x,n)); write("b058987.txt", n, " ", a); 
               ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 24 2009]
%Y A058987 A000108(n) - A001006(n-1).
%Y A058987 Sequence in context: A113299 A126931 A071722 this_sequence A001558 A111639 
               A149029
%Y A058987 Adjacent sequences: A058984 A058985 A058986 this_sequence A058988 A058989 
               A058990
%K A058987 nonn
%O A058987 1,3
%A A058987 You Seng Peng (giawgwan(AT)single.url.com.tw), Jan 17 2001

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