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 A371406 #16 Dec 25 2024 09:17:04
%S A371406 1,6,49,462,4734,51216,575705,6657846,78703438,946740132,11551512042,
%T A371406 142616584380,1778372098000,22365031140900,283341912929865,
%U A371406 3612782260978470,46326552943960278,597034029166804068,7728885814331709374,100458438481544424996
%N A371406 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^2 ) ).
%H A371406 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371406 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(2*(n+1),k) * binomial(2*(n+1),n-k).
%F A371406 a(n) = A219538(n+1)/2. - _Seiichi Manyama_, Dec 24 2024
%F A371406 a(n) = (1/(n+1)) * [x^n] ( (1+x) * (1+2*x) )^(2*(n+1)). - _Seiichi Manyama_, Dec 25 2024
%o A371406 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+2*x)^2))/x)
%o A371406 (PARI) a(n) = sum(k=0, n, 2^k*binomial(2*(n+1), k)*binomial(2*(n+1), n-k))/(n+1);
%Y A371406 Cf. A219538, A371398.
%Y A371406 Cf. A379546, A379547.
%K A371406 nonn
%O A371406 0,2
%A A371406 _Seiichi Manyama_, Mar 21 2024