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 A378467 #10 Nov 27 2024 08:06:14
%S A378467 1,1,3,12,53,249,1223,6207,32296,171355,923583,5042840,27834231,
%T A378467 155052721,870594423,4921968177,27995045409,160080985928,919731472614,
%U A378467 5306779508096,30737417720495,178654274650097,1041678247875531,6091298104643577,35714017347725474
%N A378467 Expansion of (1/x) * Series_Reversion( x * (1 - x - x^2/(1 - x)^2) ).
%H A378467 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A378467 G.f.: exp( Sum_{k>=1} A378462(k) * x^k/k ).
%F A378467 a(n) = (1/(n+1)) * [x^n] 1/(1 - x - x^2/(1 - x)^2)^(n+1).
%F A378467 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(2*n+k,n-2*k).
%o A378467 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2/(1-x)^2))/x)
%o A378467 (PARI) a(n) = sum(k=0, n\2, binomial(n+k, k)*binomial(2*n+k, n-2*k))/(n+1);
%Y A378467 Cf. A001002, A001003.
%Y A378467 Cf. A378462.
%K A378467 nonn
%O A378467 0,3
%A A378467 _Seiichi Manyama_, Nov 27 2024