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 A371364 #15 Apr 22 2024 12:48:45
%S A371364 1,5,49,597,8129,118469,1807665,28512213,461141761,7606159365,
%T A371364 127454706609,2163636679125,37130370808257,643099703566277,
%U A371364 11227141735655345,197356077159062613,3490230884900117505,62054912214781757957,1108568475427756051761
%N A371364 Expansion of (1/x) * Series_Reversion( x * (1-4*x)^2 / (1-3*x) ).
%H A371364 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371364 a(n) = (1/(n+1)) * Sum_{k=0..n} 3^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).
%F A371364 D-finite with recurrence (n+1)*(2*n+1)*a(n) +3*(-6*n^2-9*n+2)*a(n-1) -27*(7*n-9)*(2*n-3)*a(n-2) -243*(n-2)*(2*n-5)*a(n-3)=0. - _R. J. Mathar_, Apr 22 2024
%p A371364 A371364 := proc(n)
%p A371364 add(3^(n-k)*binomial(2*n+k+1,k)*binomial(2*n,n-k),k=0..n) ;
%p A371364 %/(n+1) ;
%p A371364 end proc:
%p A371364 seq(A371364(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o A371364 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^2/(1-3*x))/x)
%o A371364 (PARI) a(n) = sum(k=0, n, 3^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);
%Y A371364 Cf. A059231, A371365.
%K A371364 nonn
%O A371364 0,2
%A A371364 _Seiichi Manyama_, Mar 19 2024