%I #17 Sep 26 2022 08:19:34
%S 1,2,18,264,5400,141840,4551120,172529280,7545363840,373944211200,
%T 20711190931200,1267784551756800,84991791159475200,
%U 6193091146059417600,487361761916020992000,41192820513212239872000,3721763273059549605888000,357950394802026289815552000
%N Doubles (index 2+) under "AIJ" (ordered, indistinct, labeled) transform.
%H Andrew Howroyd, <a href="/A032037/b032037.txt">Table of n, a(n) for n = 1..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=92">Encyclopedia of Combinatorial Structures 92</a>
%F a(n) = n!*A001003(n-1). - _Vladeta Jovovic_, Dec 06 2002
%F E.g.f.: series reversion of x*(1-2*x)/(1-x). - _Andrew Howroyd_, Sep 19 2018
%F Assuming offset = 0:
%F a(n) = Sum_{k=0..n} Sum{m=0..k} (-1)^(m + k) * binomial(n + k, n + m) * binomial(n + m - 1, m - 1) * (n + m)! / m!. - _Peter Luschny_, Sep 26 2022
%t a[1]=1; a[2]=2; a[n_] := a[n]=3(2n-3)a[n-1]-(n-1)(n-3)a[n-2]
%o (PARI) Vec(serlaplace(serreverse(x*(1-2*x)/(1-x) + O(x^20)))) \\ _Andrew Howroyd_, Sep 19 2018
%K nonn
%O 1,2
%A _Christian G. Bower_
%E Terms a(17) and beyond from _Andrew Howroyd_, Sep 19 2018