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A122972 a(1) = 1, a(2) = 2; for n>2, a(n+1) = a(n)*(n-1) + a(n-1)*n.

%I A122972 #16 Nov 21 2013 12:49:00
%S A122972 1,2,4,14,58,302,1858,13262,107698,980942,9905458,109844942,
%T A122972 1327159858,17353902542,244180971058,3678842132942,59089527531058,
%U A122972 1007972756756942,18199148360427058,346736152866068942
%N A122972 a(1) = 1, a(2) = 2; for n>2, a(n+1) = a(n)*(n-1) + a(n-1)*n.
%C A122972 a(n+2) - a(n) = 3*(n-1)*(n-1)! = A052673(n).
%H A122972 Reinhard Zumkeller, <a href="/A122972/b122972.txt">Table of n, a(n) for n = 1..250</a>
%F A122972 a(n) = 2*(-1)^n - 3*(-1)^n*Sum_{k=0..n-1} (-1)^k*k!. - _Vaclav Kotesovec_, Oct 28 2012
%t A122972 RecurrenceTable[{a[1]==1,a[2]==2,a[n]==a[n-1](n-2)+a[n-2](n-1)}, a,{n,20}] (* _Harvey P. Dale_, Nov 02 2011 *)
%t A122972 Table[2*(-1)^n-3*(-1)^n*Sum[(-1)^k*k!,{k,0,n-1}],{n,1,20}] (* _Vaclav Kotesovec_, Oct 28 2012 *)
%o A122972 (Haskell)
%o A122972 a122972 n = a122972_list !! (n-1)
%o A122972 a122972_list = 1 : 2 : zipWith (+)
%o A122972    (zipWith (*) [2..] a122972_list) (zipWith (*) [1..] $ tail a122972_list)
%o A122972 -- _Reinhard Zumkeller_, Nov 15 2011
%K A122972 nonn
%O A122972 1,2
%A A122972 _Reinhard Zumkeller_, Sep 21 2006