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 A378427 #13 Nov 26 2024 03:00:20
%S A378427 1,1,1,2,8,29,88,253,775,2575,8797,29833,100635,342408,1181727,
%T A378427 4120223,14435969,50738813,179038408,634696939,2259677734,8072923814,
%U A378427 28924907573,103915759961,374302237154,1351541722226,4891132336481,17736792240766,64440831300682
%N A378427 Expansion of (1/x) * Series_Reversion( x / (1 + x + x^3 * (1 + x)^3) ).
%H A378427 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A378427 G.f.: exp( Sum_{k>=1} A378407(k) * x^k/k ).
%F A378427 a(n) = (1/(n+1)) * [x^n] (1 + x + x^3 * (1 + x)^3)^(n+1).
%F A378427 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(n+2*k+1,n-3*k).
%o A378427 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^3*(1+x)^3))/x)
%o A378427 (PARI) a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(n+2*k+1, n-3*k))/(n+1);
%Y A378427 Cf. A300048, A378425.
%Y A378427 Cf. A198951, A378407.
%K A378427 nonn
%O A378427 0,4
%A A378427 _Seiichi Manyama_, Nov 25 2024