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 A175322 #22 Sep 08 2022 08:45:51
%S A175322 12,490,17136,584988,19889100,675741430,22955884992,779827644120,
%T A175322 26491203224556,899921193951778,30570830043692400,1038508304094967860,
%U A175322 35278711531352926572,1198437683891107427950,40711602541519349266176,1382996048732155862584368
%N A175322 a(n) = A053141(n)*A001109(n+1) = Sum_{k=A053141(n)+1..A001109(n+1)-1} k.
%C A175322 Solution to a*b = (b*(b-1) - a*(a+1))/2 in A000027 with a,b >= 2.
%H A175322 Colin Barker, <a href="/A175322/b175322.txt">Table of n, a(n) for n = 1..650</a>
%H A175322 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (41,-246,246,-41,1).
%F A175322 From _Colin Barker_, Mar 31 2018: (Start)
%F A175322 G.f.: 2*x*(2 - x)*(3 + x) / ((1 - x)*(1 - 34*x + x^2)*(1 - 6*x + x^2)).
%F A175322 a(n) = 41*a(n-1) - 246*a(n-2) + 246*a(n-3) - 41*a(n-4) + a(n-5) for n>5.
%F A175322 (End)
%F A175322 a(n) = (1 - 8*U(n, 3) + 7*U(n, 17) + U(n-1, 17)) / 16 where U(n, x) is the Chebyshev polynomial of the second kind. - _Michael Somos_, Jul 18 2018
%e A175322 A053141(1) = 2 and A001109(2) = 6, then 2*6 = 3+4+5 = 12, is a term.
%e A175322 A053141(2) = 14 and A001109(3) = 35, then 14*35 = 15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34 = 490, is a term.
%e A175322 G.f. = 12*x + 490*x^2 + 17136*x^3 + 584988*x^4 + 19889100*x^5 + ... - _Michael Somos_, Jul 18 2018
%t A175322 lst={};k=1;j=0;s=1;Do[a=6*k-j;p=2*s*a;s=s+a;AppendTo[lst,p];j=k;k=a,{n,1,16}];lst
%t A175322 LinearRecurrence[{41,-246,246,-41,1}, {12, 490, 17136, 584988, 19889100}, 30] (* _G. C. Greubel_, Jul 15 2018 *)
%t A175322 a[ n_] := (1 - 8 ChebyshevU[n, 3] + 7 ChebyshevU[n, 17] + ChebyshevU[n - 1, 17]) / 16; (* _Michael Somos_, Jul 18 2018 *)
%o A175322 (PARI) Vec(2*x*(2 - x)*(3 + x) / ((1 - x)*(1 - 34*x + x^2)*(1 - 6*x + x^2)) + O(x^20)) \\ _Colin Barker_, Mar 31 2018
%o A175322 (PARI) {a(n) = if( n>0, polcoeff( 2*x * (2 - x)*(3 + x) / ((1 - x)*(1 - 34*x + x^2)*(1 - 6*x + x^2)) + x * O(x^n), n), n=-n; polcoeff( -2*x^2 * (1-2*x)*(1+3*x) / ((1 - x)*(1 - 34*x + x^2)*(1 - 6*x + x^2)) + x * O(x^n), n))}; /* _Michael Somos_, Jul 18 2018 */
%o A175322 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(2*x*(2-x)*(3+x)/((1-x)*(1-34*x+x^2)*(1-6*x+x^2)))); // _G. C. Greubel_, Jul 15 2018
%Y A175322 Cf. A053141, A001109.
%K A175322 nonn,easy
%O A175322 1,1
%A A175322 _Manuel Valdivia_, Apr 03 2010
%E A175322 Definition simplified by _N. J. A. Sloane_, Apr 05 2010