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 A231121 #24 Feb 24 2025 23:33:03
%S A231121 1,1,15,945,175,17325,23648625,1576575,7309575,1283268987,3360942585,
%T A231121 1932541986375,135664447443525,218461268025,242856109621125,
%U A231121 27604644460267875,4479480941961650625,1151866527932995875,31580724596338947904875,809762169136896100125,4742892704944677157875
%N A231121 Denominators of coefficients of expansion of arctan(x)^3.
%F A231121 Let u(n) = (-1)^n/(2*n+1) and P(n,x) = u(n) + x*Sum_{i=0..n-1} u(i)*P(n-i-1,x), with P(0,x) = u(0). Then, the terms are the denominators of the coefficients of x^2 in each polynomial.
%t A231121 a[n_] := SeriesCoefficient[ArcTan[x]^3, {x, 0, 2*n+3}] // Denominator
%t A231121 (* or *) a[n_] := 3*Sum[2^(i-2)*Binomial[2*(n+1), i-1]*StirlingS1[i, 3]/i!, {i, 3, 2n+3}] // Denominator; Table[a[n], {n, 0, 20}] (* from the formula given by _Ruperto Corso_ in A002429 *)
%t A231121 Take[Denominator[CoefficientList[Series[ArcTan[x]^3,{x,0,50}],x] ], {4,-1,2}] (* _Harvey P. Dale_, Apr 07 2017 *)
%Y A231121 Cf. A002428, A002429, A071968, A140749, A141904, A142048, A081051.
%K A231121 nonn,frac
%O A231121 0,3
%A A231121 _Jean-François Alcover_ and _Paul Curtz_, Nov 04 2013