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 A115147 #14 Sep 08 2022 08:45:23
%S A115147 1,-8,20,-16,2,0,0,0,-1,-8,-44,-208,-910,-3808,-15504,-62016,-245157,
%T A115147 -961400,-3749460,-14567280,-56448210,-218349120,-843621600,
%U A115147 -3257112960,-12570420330,-48507033744,-187187399448,-722477682080,-2789279908316,-10772391370048
%N A115147 Eighth convolution of A115140.
%H A115147 Seiichi Manyama, <a href="/A115147/b115147.txt">Table of n, a(n) for n = 0..1670</a>
%F A115147 O.g.f.: 1/c(x)^8 = P(9, x) - x*P(8, x)*c(x) with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers) and the polynomials P(n, x) defined in A115139. Here P(9, x)= 1-7*x+15*x^2-10*x^3+x^4 and P(8, x)=1-6*x+10*x^2-4*x^3.
%F A115147 a(n) = -C8(n-8), n>=8, with C8(n) = A003518(n+3) (eighth convolution of Catalan numbers). a(0)=1, a(1)=-8, a(2)=30, a(3)=-16, a(4)=2, a(5)=a(6)=a(7)=0. [1, -8, 20, -16, 2] is row n=8 of signed A034807 (signed Lucas polynomials). See A115149 and A034807 for comments.
%t A115147 CoefficientList[Series[(1-8*x+20*x^2-16*x^3+2*x^4 +(1-6*x+10*x^2-4*x^3) *Sqrt[1-4*x])/2, {x, 0, 30}], x] (* _G. C. Greubel_, Feb 12 2019 *)
%o A115147 (PARI) my(x='x+O('x^30)); Vec((1-8*x+20*x^2-16*x^3+2*x^4 +(1-6*x+10*x^2 -4*x^3)*sqrt(1-4*x))/2) \\ _G. C. Greubel_, Feb 12 2019
%o A115147 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!( (1-8*x+20*x^2-16*x^3+2*x^4 +(1-6*x+10*x^2-4*x^3)*Sqrt(1-4*x))/2 )); // _G. C. Greubel_, Feb 12 2019
%o A115147 (Sage) ((1-8*x+20*x^2-16*x^3+2*x^4 +(1-6*x+10*x^2-4*x^3)*sqrt(1-4*x))/2 ).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Feb 12 2019
%Y A115147 Cf. A115139 - A115146, A115148, A115149.
%K A115147 sign,easy
%O A115147 0,2
%A A115147 _Wolfdieter Lang_, Jan 13 2006