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 A115140 O.g.f. inverse of Catalan A000108 o.g.f. 13

%I

%S 1,-1,-1,-2,-5,-14,-42,-132,-429,-1430,-4862,-16796,-58786,-208012,

%T -742900,-2674440,-9694845,-35357670,-129644790,-477638700,

%U -1767263190,-6564120420,-24466267020,-91482563640,-343059613650,-1289904147324,-4861946401452,-18367353072152

%N O.g.f. inverse of Catalan A000108 o.g.f.

%H Seiichi Manyama, <a href="/A115140/b115140.txt">Table of n, a(n) for n = 0..1668</a>

%F See A034807 and A115149 for comments.

%F For convolutions of this sequence see A115141-A115149.

%F O.g.f.: 1/c(x) = 1-x*c(x) with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).

%F a(0) = 1, a(n) = -C(n-1), n>=1, with C(n):=A000108(n) (Catalan).

%F G.f.: (1 + sqrt(1-4*x))/2=U(0) where U(k)=1 - x/U(k+1) ; (continued fraction, 1-step). - _Sergei N. Gladkovskii_, Oct 29 2012

%F G.f.: 1/G(0) where G(k) = 1 - x/(x - 1/G(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Dec 12 2012

%F G.f.: G(0), where G(k)= 2*x*(2*k+1) + k + 1 - 2*x*(k+1)*(2*k+3)/G(k+1) ; (continued fraction). - _Sergei N. Gladkovskii_, Jul 14 2013

%F n*a(n) +2*(-2*n+3)*a(n-1)=0. a(n) = A002420(n)/2, n>0. - _R. J. Mathar_, Aug 09 2015

%K sign,easy

%O 0,4

%A _Wolfdieter Lang_, Jan 13 2006

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Last modified October 23 17:20 EDT 2018. Contains 316529 sequences. (Running on oeis4.)