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 A372110 #18 Nov 30 2024 08:49:57
%S A372110 1,3,30,381,5457,84000,1356726,22680705,389100000,6811276449,
%T A372110 121177168266,2184600000000,39822674320065,732762138176436,
%U A372110 13592289000000000,253896500477864361,4771765283550516435,90167361600000000000,1712019315455953465026
%N A372110 G.f. A(x) satisfies A(x) = ( (1 - x*A(x))/(1 - 10*x*A(x)) )^(1/3).
%H A372110 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A372110 a(n) = (1/(n+1)) * Sum_{k=0..n} 9^k * binomial(n/3+k-2/3,k) * binomial(n-1,n-k).
%F A372110 From _Seiichi Manyama_, Nov 30 2024: (Start)
%F A372110 G.f.: exp( Sum_{k>=1} A378552(k) * x^k/k ).
%F A372110 a(n) = (1/(n+1)) * [x^n] 1/(1 - 9*x/(1-x))^((n+1)/3).
%F A372110 G.f.: (1/x) * Series_Reversion( x*(1 - 9*x/(1-x))^(1/3) ). (End)
%o A372110 (PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3+k-2/3, k)*binomial(n-1, n-k))/(n+1);
%Y A372110 Cf. A001003, A372109.
%Y A372110 Cf. A361375, A372019, A372091, A372105, A378552.
%K A372110 nonn
%O A372110 0,2
%A A372110 _Seiichi Manyama_, Apr 19 2024