cp's OEIS Frontend

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

%I A115140 #38 Jul 02 2021 16:51:41
%S A115140 1,-1,-1,-2,-5,-14,-42,-132,-429,-1430,-4862,-16796,-58786,-208012,
%T A115140 -742900,-2674440,-9694845,-35357670,-129644790,-477638700,
%U A115140 -1767263190,-6564120420,-24466267020,-91482563640,-343059613650,-1289904147324,-4861946401452,-18367353072152
%N A115140 O.g.f. inverse of Catalan A000108 o.g.f.
%H A115140 Seiichi Manyama, <a href="/A115140/b115140.txt">Table of n, a(n) for n = 0..1668</a>
%H A115140 Paul Barry, <a href="https://arxiv.org/abs/2004.04577">On a Central Transform of Integer Sequences</a>, arXiv:2004.04577 [math.CO], 2020.
%H A115140 Paul Barry, <a href="https://arxiv.org/abs/2104.01644">Centered polygon numbers, heptagons and nonagons, and the Robbins numbers</a>, arXiv:2104.01644 [math.CO], 2021.
%H A115140 Ângela Mestre and José Agapito, <a href="https://www.emis.de/journals/JIS/VOL22/Agapito/mestre8.html">A Family of Riordan Group Automorphisms</a>, J. Int. Seq., Vol. 22 (2019), Article 19.8.5.
%F A115140 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 A115140 a(0) = 1, a(n) = -C(n-1), n>=1, with C(n):=A000108(n) (Catalan).
%F A115140 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 A115140 G.f.: 1/G(0) where G(k) = 1 - x/(x - 1/G(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Dec 12 2012
%F A115140 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 A115140 D-finite with recurrence n*a(n) +2*(-2*n+3)*a(n-1)=0. a(n) = A002420(n)/2, n>0. - _R. J. Mathar_, Aug 09 2015
%F A115140 a(n) ~ -2^(2*n-2) / (sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, May 06 2021
%Y A115140 See A034807 and A115149 for comments.
%Y A115140 For convolutions of this sequence see A115141-A115149.
%K A115140 sign,easy
%O A115140 0,4
%A A115140 _Wolfdieter Lang_, Jan 13 2006