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 A386771 #12 Aug 03 2025 11:20:54
%S A386771 1,18,474,14732,502401,18180768,685607224,26650023732,1060231986276,
%T A386771 42960995865518,1766880793326474,73566710202432732,
%U A386771 3094892737300954526,131352228574805862768,5617341984325110170724,241825069451020881591732,10471314920765093871735276
%N A386771 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^3 / (1+3*x)^4 ).
%H A386771 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A386771 a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * 2^(n-k) * binomial(4*(n+1),k) * binomial(4*n-k+2,n-k).
%F A386771 a(n) = (1/(n+1)) * [x^n] ( (1+3*x)^4 / (1-2*x)^3 )^(n+1).
%F A386771 D-finite with recurrence +168*(3*n+2)*(3*n+1)*(n+1)*a(n) +(-204763*n^3 +291562*n^2 -58913*n +7322)*a(n-1) +3*(2113057*n^3 -10391714*n^2 +14167979*n -5959810)*a(n-2) +15*(939475*n^3 +13499790*n^2 -61292611*n +62827794)*a(n-3) -22987800*(2*n-5)*(4*n-9)*(4*n-11)*a(n-4)=0. - _R. J. Mathar_, Aug 03 2025
%o A386771 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^3/(1+3*x)^4)/x)
%o A386771 (PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);
%Y A386771 Cf. A386774.
%K A386771 nonn
%O A386771 0,2
%A A386771 _Seiichi Manyama_, Aug 02 2025