This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217477 #21 Jun 01 2025 19:53:57 %S A217477 3,-4,12,-40,140,-504,1848,-6864,25740,-97240,369512,-1410864,5408312, %T A217477 -20801200,80233200,-310235040,1202160780,-4667212440,18150270600, %U A217477 -70690527600,275693057640,-1076515748880,4208197927440,-16466861455200 %N A217477 Z-sequence for the Riordan triangle A111125. %C A217477 For the notion Z-sequence for a Riordan triangle (lower triangular matrix) R(n,m) see a W.Lang link under A006232, with references. The Z-sequence appears in the recurrence for any entry R(n,0), n >= 1: R(n,0) = sum(Z(m)*R(n-1,m), m=0..n-1). %C A217477 The A-sequence for the Riordan triangle A111125 is (-1)^n*A115141(n). %F A217477 O.g.f.: (1 - (2 - c(-x))/(1 + 4*x))/(1 - c(-x)) = ((3 + 4*x) + 4*x*c(-x))/(1 + 4*x), with c(x) the o.g.f. of A000108 (Catalan). %F A217477 a(0) = 3, a(n) = ((-1)^n)*4*binomial(2*n-1,n), n >= 1, (from adding the two pieces of the second o.g.f. version). %F A217477 |a(n)| = A100320(n), n >0. - _R. J. Mathar_, Apr 22 2013 %F A217477 G.f.: 1 + G(0), where G(k)= 1 + 1/(1 - 2*x*(2*k+1)/(2*x*(2*k+1) - (k+1)/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 24 2013 %Y A217477 Cf.: A111125, A115141. %K A217477 sign,easy %O A217477 0,1 %A A217477 _Wolfdieter Lang_, Oct 18 2012