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 A157125 #11 Oct 05 2024 16:31:25
%S A157125 1,-1,-1,0,2,1,-1,-4,-2,4,12,4,-20,-39,3,92,118,-84,-388,-308,596,
%T A157125 1528,508,-3292,-5556,1154,16034,17940,-18160,-71243,-45913,127124,
%U A157125 290278,46128,-710864,-1067564,485108,3504680,3362756,-4957812,-15669148
%N A157125 A transform of the Catalan numbers.
%C A157125 Hankel transform is A157126. Partial sums are A157127.
%F A157125 G.f.: (1-x)*(sqrt(1+x^2+4*x^3)-sqrt(1+x^2))/(2*x^3*sqrt(1+x^2));
%F A157125 a(n) = Sum_{k=0..n} (-1)^binomial(n-k+1,2)*binomial(floor((n-k)/2),k)*A000108(k).
%F A157125 Conjecture: (n+3)*(n-2)*a(n) -4*a(n-1) +2*(n^2-n-4)*a(n-2) +2*(2*n^2-7*n+2)*a(n-3) +(n+1)*(n-4)*a(n-4) +2*(n-1)*(2*n-7)*a(n-5)=0. - _R. J. Mathar_, Nov 15 2012
%Y A157125 Cf. A000108, A157126, A157127.
%K A157125 easy,sign
%O A157125 0,5
%A A157125 _Paul Barry_, Feb 23 2009
%E A157125 Divisor x^3 inserted in the g.f. - _R. J. Mathar_, Feb 06 2015