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 A181474 #16 Jul 25 2023 10:58:49
%S A181474 1,2,10,15,42,56,120,150,275,330,546,637,980,1120,1632,1836,2565,2850,
%T A181474 3850,4235,5566,6072,7800,8450,10647,11466,14210,15225,18600,19840,
%U A181474 23936,25432,30345,32130,37962,40071,46930
%N A181474 Sequence related to the Hankel transform of A105523(n+5).
%C A181474 The Hankel transform of A105523(n+5) is (-1)^C(n+2,2)a(n+1).
%H A181474 Michael De Vlieger, <a href="/A181474/b181474.txt">Table of n, a(n) for n = 0..10000</a>
%H A181474 Nathaniel K. Green and Edward D. Kim, <a href="https://arxiv.org/abs/2307.06311">Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala</a>, arXiv:2307.06311 [math.OC], 2023. See p. 18.
%H A181474 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).
%F A181474 G.f.: (1+x+4x^2+x^3+x^4)/((1-x)^5(1+x)^4);
%F A181474 a(n) = 2^n*(n+2)*(n+3)*Gamma(floor(n/2)+3)*Gamma(floor((n+1)/2)+1/2)/(12n!*sqrt(Pi)) (suggested by WolframAlpha).
%F A181474 a(n) = +a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9). a(n) = (n+3)*(n+2)*(2*n^2+2*(-1)^n*n+10*n+5*(-1)^n+11)/96. [_R. J. Mathar_, Oct 23 2010]
%t A181474 CoefficientList[Series[(1 + x + 4 x^2 + x^3 + x^4)/((1 - x)^5 (1 + x)^4), {x, 0, 36}], x] (* _Michael De Vlieger_, Jul 25 2023 *)
%K A181474 easy,nonn
%O A181474 0,2
%A A181474 _Paul Barry_, Oct 22 2010