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 A382042 #19 Mar 14 2025 08:58:57
%S A382042 1,1,3,37,733,20181,714541,30903769,1579206441,93099946249,
%T A382042 6219777779641,464382363698661,38319628830696973,3463058939163189133,
%U A382042 340172205752538636933,36087128101110502864561,4111807211977470782285521,500807663307856030823859729,64931674940413564774656214513
%N A382042 E.g.f. A(x) satisfies A(x) = exp(x*C(x*A(x)^3)), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
%F A382042 Let F(x) be the e.g.f. of A382039. F(x) = log(A(x))/x = C(x*A(x)^3).
%F A382042 E.g.f.: A(x) = exp( Series_Reversion( x*(1 - x*exp(3*x)) ) ).
%F A382042 a(n) = n! * Sum_{k=0..n-1} (3*k+1)^(n-k-1) * binomial(n+k,k)/((n+k) * (n-k-1)!) for n > 0.
%o A382042 (PARI) a(n) = if(n==0, 1, n!*sum(k=0, n-1, (3*k+1)^(n-k-1)*binomial(n+k, k)/((n+k)*(n-k-1)!)));
%Y A382042 Cf. A161629, A382029.
%Y A382042 Cf. A000108, A212917, A382039.
%K A382042 nonn
%O A382042 0,3
%A A382042 _Seiichi Manyama_, Mar 13 2025