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 A119374 #7 Mar 17 2021 08:02:47
%S A119374 1,3,10,36,133,501,1918,7440,29180,115522,461044,1852938,7492846,
%T A119374 30464306,124461782,510696350,2103708187,8696498477,36066269640,
%U A119374 150015248758,625664295594,2615929689642,10962436020878,46037427169060
%N A119374 A lower diagonal of pendular trinomial triangle A119369.
%H A119374 G. C. Greubel, <a href="/A119374/b119374.txt">Table of n, a(n) for n = 0..1000</a>
%F A119374 G.f.: A(x) = B(x)^3/(1+x - x*B(x)) = B(x)^3*G(x) = B(x)^2*H(x) = B(x)*I(x), where B(x) is g.f. of A119370, G(x) is g.f. of A119371, H(x) is g.f. of A119372 and I(x) is g.f. of A119373.
%F A119374 G.f.: 16*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ).
%t A119374 CoefficientList[Series[16*(1+x)/( ((1+x^2) +Sqrt[(1+x^2)^2 -4*x*(1+x)])^3*(1+4*x +x^2 +Sqrt[(1+4*x+x^2)^2 -4*x*(1+x)*(3+2*x)])), {x,0,30}], x] (* _G. C. Greubel_, Mar 16 2021 *)
%o A119374 (PARI) {a(n)=polcoeff(16*(1+x)/((1+x^2)+sqrt((1+x^2)^2-4*x*(1+x)+x*O(x^n)))^3 /(1+4*x+x^2 + sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x)+x*O(x^n))),n)}
%o A119374 (Sage)
%o A119374 def A119374_list(prec):
%o A119374 P.<x> = PowerSeriesRing(QQ, prec)
%o A119374 return P( 16*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ) ).list()
%o A119374 A119374_list(30) # _G. C. Greubel_, Mar 16 2021
%o A119374 (Magma)
%o A119374 R<x>:=PowerSeriesRing(Rationals(), 30);
%o A119374 Coefficients(R!( 16*(1+x)/( ((1+x^2) +Sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +Sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ) )); // _G. C. Greubel_, Mar 16 2021
%Y A119374 Cf. A119369, A119370, A119371, A119372, A119373, A119375, A119376.
%K A119374 nonn
%O A119374 0,2
%A A119374 _Paul D. Hanna_, May 17 2006