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 A371428 #12 Sep 25 2024 10:50:51
%S A371428 1,3,11,46,209,1003,5002,25665,134605,718371,3888633,21298962,
%T A371428 117823660,657344600,3694378463,20896495211,118865999117,679545095167,
%U A371428 3902327585407,22499738052954,130200110475407,755927955655813,4402088019958400,25706104810367515
%N A371428 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 - x^2) ).
%H A371428 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371428 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+1,k) * binomial(3*n-3*k+3,n-2*k).
%t A371428 Table[1/(n+1) Sum[(-1)^k Binomial[n+1,k]Binomial[3n-3k+3,n-2k],{k,0,Floor[n/2]}],{n,0,30}] (* _Harvey P. Dale_, Sep 25 2024 *)
%o A371428 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3-x^2))/x)
%o A371428 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, k)*binomial(3*n-3*k+3, n-2*k))/(n+1);
%Y A371428 Cf. A107264, A127897, A371429.
%K A371428 nonn
%O A371428 0,2
%A A371428 _Seiichi Manyama_, Mar 23 2024