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 A382029 #18 Mar 14 2025 04:45:18
%S A382029 1,1,3,31,529,12601,385891,14440567,638576065,32580927505,
%T A382029 1883889232291,121742057314351,8695278706372369,680187946863332233,
%U A382029 57833833258995140803,5310742450917819399751,523793286672328763358721,55223769332070053104438945,6197871354601209094032190147
%N A382029 E.g.f. A(x) satisfies A(x) = exp(x*C(x*A(x)^2)), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
%F A382029 Let F(x) be the e.g.f. of A379690. F(x) = log(A(x))/x = C(x*A(x)^2).
%F A382029 E.g.f.: A(x) = exp( Series_Reversion( x*(1 - x*exp(2*x)) ) ).
%F A382029 a(n) = n! * Sum_{k=0..n-1} (2*k+1)^(n-k-1) * binomial(n+k,k)/((n+k) * (n-k-1)!) for n > 0.
%o A382029 (PARI) a(n) = if(n==0, 1, n!*sum(k=0, n-1, (2*k+1)^(n-k-1)*binomial(n+k, k)/((n+k)*(n-k-1)!)));
%Y A382029 Cf. A212722, A382030, A382031.
%Y A382029 Cf. A161629, A382042.
%Y A382029 Cf. A000108, A214688, A214689, A379690.
%K A382029 nonn
%O A382029 0,3
%A A382029 _Seiichi Manyama_, Mar 12 2025