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 A378465 #11 Nov 27 2024 07:11:57
%S A378465 1,2,9,51,324,2206,15737,116098,878495,6780544,53175176,422508607,
%T A378465 3394004192,27518168434,224899980185,1850830170355,15324273361220,
%U A378465 127562500961502,1066940307951747,8962213871074848,75572666059970392,639485384767169924,5428457500063304272
%N A378465 Expansion of (1/x) * Series_Reversion( x * (1 - x - x/(1 - x)) ).
%H A378465 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A378465 G.f.: exp( Sum_{k>=1} A378460(k) * x^k/k ).
%F A378465 a(n) = (1/(n+1)) * [x^n] 1/(1 - x - x/(1 - x))^(n+1).
%F A378465 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+k,k) * binomial(2*n+k,n-k).
%F A378465 a(n) ~ ((16 + 12*2^(1/3) + 9*2^(2/3))/5)^n / (sqrt(6*(4 - 3*2^(1/3))*Pi) * n^(3/2)). - _Vaclav Kotesovec_, Nov 27 2024
%o A378465 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x/(1-x)))/x)
%o A378465 (PARI) a(n) = sum(k=0, n, binomial(n+k, k)*binomial(2*n+k, n-k))/(n+1);
%Y A378465 Cf. A151374, A378466.
%Y A378465 Cf. A378460.
%K A378465 nonn
%O A378465 0,2
%A A378465 _Seiichi Manyama_, Nov 27 2024