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 A119429 #24 Apr 09 2022 06:43:57
%S A119429 1,0,1,2,5,14,45,164,661,2884,13461,66894,353217,1977146,11691481,
%T A119429 72734088,474172777,3229062120,22914397417,169128976922,1296276808253,
%U A119429 10300677006854,84731125615749,720392483485868,6321631421441149
%N A119429 Expansion of Sum_{k>=0} x^(2*k)/Product_{j=1..k} (1 - j*2*x).
%H A119429 Seiichi Manyama, <a href="/A119429/b119429.txt">Table of n, a(n) for n = 0..588</a>
%F A119429 a(n) = Sum_{k=0..n} S2(k,n-k)*2^(2k-n) where S2(n,k)=A048993(n,k).
%F A119429 a(n) = Sum_{k=0..floor(n/2)} S2(n-k,k)*2^(n-2k) where S2(n,k)=A048993(n,k).
%F A119429 Let E(x) = Sum_{k>=0} x^(2*k)/Product_{j=1..k} (1 - j*2*x), then E(x) = 1 + x^2/(U(0)-x^2), where U(k) = (x-1)^2 - 2*k*x + x^2*(2*k*x + 2*x - 1)/U(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Jun 26 2012
%F A119429 G.f.: 1 + x*(G(0) - 1)/(x-1) where G(k) = 1 - x/(1-x*(2*k+2))/(1-x/(x-1/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jan 16 2013
%o A119429 (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*stirling(n-k, k, 2)); \\ _Seiichi Manyama_, Apr 08 2022
%Y A119429 Cf. A024427, A048993.
%K A119429 easy,nonn
%O A119429 0,4
%A A119429 _Paul Barry_, May 19 2006