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%I #9 May 26 2023 13:20:48
%S 0,1,2,10,66,568,6010,75528,1099462,18195616,337416246,6930281080,
%T 156177762466,3831429672144,101647482387802,2899769522268472,
%U 88517797903871190,2878965845280173632,99389641303891713718
%N a(n) = 2*(n-1)*a(n-1)+(n-1)*a(n-2) with a(0)=0, a(1)=1.
%C This is also the (2,2) element of the product matrix after multiplying the unit matrix from the left by the matrices (0,1;j-1,2j-2) in the order j=2 to n.
%t M[n_] := {{0, 1}, {(n - 1), 2*(n - 1)}} v[1] = {0, 1} v[n_] := v[n] = M[n].v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 25}]
%t nxt[{n_,a_,b_}]:={n+1,b,2n*b+n*a}; NestList[nxt,{1,0,1},20][[;;,2]] (* _Harvey P. Dale_, May 26 2023 *)
%Y Cf. A000166.
%K nonn,easy
%O 0,3
%A _Roger L. Bagula_, Jun 15 2005
%E Definition substituted by G. Detlefs' recurrence by the Associate Editors of the OEIS, Sep 28 2009