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 A289428 #12 Dec 27 2019 09:58:13
%S A289428 1,3,18,144,1368,14688,173664,2226528,30647808
%N A289428 Sum of factorial-Catalan numbers over a certain family of decorations.
%C A289428 The precise definition involves the use of certain symbols akin to the peace symbol.
%H A289428 Vincent Pilaud, V. Pons, <a href="http://arxiv.org/abs/1606.09643">Permutrees</a>, arXiv preprint arXiv:1606.09643 [math.CO], 2016.
%F A289428 From _Peter Bala_, Dec 25 2019: (Start)
%F A289428 The following are conjectural (Cf. A145879):
%F A289428 Recurrence: a(n) = n*a(n-1) + 2*Sum_{k = 1..n} a(k-1)*a(n-k) with a(0) = 1.
%F A289428 O.g.f. as a regular C-fraction: 1/(1 - 3*x/(1 - 3*x/(1 - 4*x/(1 - 4*x/(1 - 5*x/(1 - 5*x/(1 - ... ))))))). Cf. A111537.
%F A289428 exp( Sum_{n >= 1} a(n)*(2*x)^n/n ) = 1 + 6*x + 54*x^2 + 636*x^3 + ... appears to have integer coefficients. (End)
%Y A289428 Cf. A289427, A289429, A289430, A289431, A000142, A111537, A145879.
%K A289428 nonn,more
%O A289428 0,2
%A A289428 _N. J. A. Sloane_, Jul 06 2017