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 A371405 #9 Mar 22 2024 09:00:15
%S A371405 1,10,136,2134,36379,654670,12239560,235407070,4627854244,92576970280,
%T A371405 1878395043232,38564373070090,799651963174978,16722655896174004,
%U A371405 352289843771100400,7469327989417602862,159263992188702829900,3412969567344634872952
%N A371405 Expansion of (1/x) * Series_Reversion( x / ( (1+x) * (1+3*x)^3 ) ).
%H A371405 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371405 a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(3*(n+1),k) * binomial(n+1,n-k).
%o A371405 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+3*x)^3))/x)
%o A371405 (PARI) a(n) = sum(k=0, n, 3^k*binomial(3*(n+1), k)*binomial(n+1, n-k))/(n+1);
%Y A371405 Cf. A364923.
%K A371405 nonn
%O A371405 0,2
%A A371405 _Seiichi Manyama_, Mar 21 2024