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 A367413 #18 Nov 27 2024 08:50:28
%S A367413 1,1,2,6,22,87,356,1493,6398,27936,123906,556734,2528668,11590555,
%T A367413 53545932,249065874,1165482126,5482782933,25914899804,123009541412,
%U A367413 586121731150,2802470267460,13441993044464,64660400422341,311861855749484,1507802756171072,7306422899878394
%N A367413 Expansion of (1/x) * Series_Reversion( x * (1-x-x^3/(1-x)^2) ).
%H A367413 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A367413 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(2*n,n-3*k).
%F A367413 From _Seiichi Manyama_, Nov 27 2024: (Start)
%F A367413 G.f.: exp( Sum_{k>=1} A378464(k) * x^k/k ).
%F A367413 a(n) = (1/(n+1)) * [x^n] 1/(1 - x - x^3/(1 - x)^2)^(n+1). (End)
%o A367413 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^3/(1-x)^2))/x)
%o A367413 (PARI) a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n, n-3*k))/(n+1);
%Y A367413 Cf. A378464.
%Y A367413 Cf. A049140, A054515.
%Y A367413 Cf. A378466, A378467.
%K A367413 nonn
%O A367413 0,3
%A A367413 _Seiichi Manyama_, Jan 26 2024