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 A371416 #18 Mar 23 2024 10:51:53
%S A371416 1,3,18,136,1152,10458,99472,978453,9871686,101590654,1062271704,
%T A371416 11253818628,120535386692,1303045817184,14199323523912,
%U A371416 155805565801803,1720024043803542,19090440094335912,212897898182054224,2384431948345110510,26808516659219953680
%N A371416 Expansion of (1/x) * Series_Reversion( x * (1 - 3*x - x^3) ).
%H A371416 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371416 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} 3^k * binomial(n+k,k) * binomial(4*n+k+2,n-2*k).
%F A371416 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} 3^(n-3*k) * binomial(n+k,k) * binomial(2*n-2*k,n-3*k).
%o A371416 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-3*x-x^3))/x)
%o A371416 (PARI) a(n) = sum(k=0, n\2, 3^k*binomial(n+k, k)*binomial(4*n+k+2, n-2*k))/(n+1);
%o A371416 (PARI) a(n) = sum(k=0, n\3, 3^(n-3*k)*binomial(n+k, k)*binomial(2*n-2*k, n-3*k))/(n+1);
%Y A371416 Cf. A049140, A120985.
%K A371416 nonn
%O A371416 0,2
%A A371416 _Seiichi Manyama_, Mar 23 2024