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 A225435 #37 Feb 16 2025 08:33:19
%S A225435 1,1,2,4,7,19,68,44,416,758,6092,24284,10348,110864,997828,4545476,
%T A225435 827252,5166356,255994804,1289266004,3332578444,8757252244,3766552348,
%U A225435 27079574548,1434303566956,4061479240156,46849154788124,54858398447372,816458740546228,189647639388428
%N A225435 Numerators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ ...)))).
%H A225435 Seiichi Manyama, <a href="/A225435/b225435.txt">Table of n, a(n) for n = 1..843</a>
%H A225435 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFractionConstants.html">Continued Fraction Constants</a>
%H A225435 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedContinuedFraction.html">Generalized Continued Fraction</a>
%F A225435 E.g.f.: (1/2)*(-2+e^((1/2)*z*(2+z))*(1+z)(2+sqrt(2*e*Pi)*erf(1/sqrt(2)))-e^((1/2)*(1+z)^2)*sqrt(2*Pi)*(1+z)*erf((1+z)/sqrt(2))).
%F A225435 Lim_{n->infinity} A225435(n)/A225436(n) = sqrt(2/(e*Pi))/erfc(1/sqrt(2))-1 = A111129.
%e A225435 1, 1/3, 2/3, 4/9, 7/12, 19/39, ... = A225435(n)/A225436(n).
%t A225435 Numerator[Table[ContinuedFractionK[k, 1, {k, 1, n}], {n, 30}]]
%Y A225435 Cf. A225436 (denominators).
%Y A225435 Cf. A111129 (decimal digits of infinite c.f.).
%Y A225435 Related to A000932.
%K A225435 nonn,frac
%O A225435 1,3
%A A225435 _Eric W. Weisstein_, May 07 2013