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 A381982 #19 Mar 14 2025 08:59:01
%S A381982 1,2,11,139,2829,78981,2802163,120667667,6113752025,356342305465,
%T A381982 23488872131871,1727770084512495,140302645206245701,
%U A381982 12466960491079733237,1203253101643330233707,125351056198801059896491,14019427299278115378992049,1675439381194882102492648305
%N A381982 E.g.f. A(x) satisfies A(x) = exp(x) * C(x*A(x)), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
%F A381982 Let F(x) be the e.g.f. of A364983. F(x) = C(x*A(x)) = exp( 1/2 * Sum_{k>=1} binomial(2*k,k) * (x*A(x))^k/k ).
%F A381982 a(n) = n! * Sum_{k=0..n} (k+1)^(n-k) * A001764(k)/(n-k)!.
%o A381982 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(n-k)*binomial(3*k+1, k)/((3*k+1)*(n-k)!));
%Y A381982 Cf. A349640, A381983.
%Y A381982 Cf. A000108, A001764, A161629, A364983.
%K A381982 nonn
%O A381982 0,2
%A A381982 _Seiichi Manyama_, Mar 11 2025