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 A379024 #14 Dec 14 2024 07:10:23
%S A379024 1,8,100,1500,24846,438064,8062518,153117320,2978260865,59031215508,
%T A379024 1187987779084,24210092837648,498606095949315,10361291534825800,
%U A379024 216982960825089730,4574651332139656108,97018731642209493810,2068350691029593934000,44301394943232879298360
%N A379024 Expansion of (1/x) * Series_Reversion( x * ((1 - x - x^2)/(1 + x))^4 ).
%H A379024 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A379024 G.f. A(x) satisfies:
%F A379024 (1) A(x) = exp( Sum_{k>=1} A379026(k) * x^k/k ).
%F A379024 (2) A(x) = ( (1 + x*A(x)) * (1 + x*A(x)^(5/4)) )^4.
%F A379024 (3) A(x) = B(x)^4 where B(x) is the g.f. of A239108.
%F A379024 a(n) = (1/(n+1)) * [x^n] ( (1 + x)/(1 - x - x^2) )^(4*(n+1)).
%F A379024 a(n) = 4 * Sum_{k=0..n} binomial(4*n+k+4,k) * binomial(4*n+k+4,n-k)/(4*n+k+4) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(4*n+k+4,n-k).
%o A379024 (PARI) a(n) = 4*sum(k=0, n, binomial(4*n+k+4, k)*binomial(4*n+k+4, n-k)/(4*n+k+4));
%Y A379024 Cf. A007863, A379021, A379023.
%Y A379024 Cf. A239108, A379026.
%K A379024 nonn
%O A379024 0,2
%A A379024 _Seiichi Manyama_, Dec 14 2024