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 A385475 #21 Aug 01 2025 08:59:58
%S A385475 1,10,154,2836,57601,1244584,28063288,652821724,15551944804,
%T A385475 377503375150,9303441938506,232168129150420,5854967533764766,
%U A385475 148981015820615968,3820184959840942564,98616983735455104412,2560818171703792341484,66845502538144505160040
%N A385475 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^3 / (1+x)^4 ).
%H A385475 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A385475 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^(n-k) * binomial(4*(n+1),k) * binomial(4*n-k+2,n-k).
%F A385475 a(n) = (1/(n+1)) * [x^n] ( (1+x)^4 / (1-2*x)^3 )^(n+1).
%o A385475 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^3/(1+x)^4)/x)
%o A385475 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);
%Y A385475 Cf. A064063, A385474.
%Y A385475 Cf. A386723.
%K A385475 nonn
%O A385475 0,2
%A A385475 _Seiichi Manyama_, Aug 01 2025