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 A266579 #21 Feb 16 2025 08:33:28
%S A266579 2,11,67,460,3532,30225,286289,2979896,33852226,417123475,5543942107,
%T A266579 79086006756,1205573749892,19561113090785,336643494142657,
%U A266579 6125614986385360,117514626855080914,2370682022353448571,50173196512398036851,1111614380526424428380
%N A266579 Numerator of the continued fraction [Sum_{k=0..n} k; 1, 2, 3,..., n].
%H A266579 Ilya Gutkovskiy, <a href="/A266579/a266579.pdf">Extended example</a>
%H A266579 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFractionConstant.html">Continued Fraction Constant</a>
%H A266579 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>
%F A266579 a(n) = A001040(n+1)*A000217(n) + A001053(n+1).
%e A266579 2, 11/3, 67/10, 460/43, 3532/225, 30225/1393, 286289/9976, 2979896/81201, 33852226/740785, 417123475/7489051, 5543942107/83120346, 79086006756/1004933203, 1205573749892/13147251985, 19561113090785/185066460993,...
%e A266579 a(10) = 417123475 because 55+1/(1+1/(2+1/(3+1/(4+1/(5+1/(6+1/(7+1/(8+1/(9+1/10))))))))) = 417123475/7489051 and 1+2+3+4+5+6+7+8+9+10 = 55.
%t A266579 Table[Numerator[n ((n + 1)/2) + ContinuedFractionK[1, k, {k, n}]], {n, 20}]
%Y A266579 Cf. A000217, A001040 (denominator, offset 2), A001053, A052119.
%K A266579 nonn,frac
%O A266579 1,1
%A A266579 _Ilya Gutkovskiy_, May 07 2016