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 A115151 #13 Apr 11 2023 13:37:02
%S A115151 1,31,289,2271,16929,123871,901153,6553567,47759393,349143007,
%T A115151 2561474593,18860670943,139371085857,1033405464543,7687240679457,
%U A115151 57356977176543,429173772386337,3219806849335263,24215844242325537
%N A115151 Fourth diagonal (M=4) sequence of triangle A113647, called Y(2,1).
%H A115151 Vincenzo Librandi, <a href="/A115151/b115151.txt">Table of n, a(n) for n = 0..300</a>
%F A115151 a(n) = A113647(n+3, n+1), n>=0.
%F A115151 G.f.: ((-2 + 8*x +x^3) + 2*(1-6*x+4*x^2)*c(2*x))/((x^3)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).
%F A115151 Recurrence: (n-1)*(n+4)*a(n) = (7*n^2 + 9*n + 8)*a(n-1) + 4*(n+1)*(2*n+1)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A115151 a(n) ~ 5*2^(3*n+9)/(9*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 19 2012
%t A115151 CoefficientList[Series[((-2+8*x+x^3)+2*(1-6*x+4*x^2)*(1-Sqrt[1-8*x])/(4*x))/((x^3)*(1+x)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 19 2012 *)
%Y A115151 Cf. A000108, A113647.
%K A115151 nonn,easy
%O A115151 0,2
%A A115151 _Wolfdieter Lang_, Jan 13 2006