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a(0)=0, a(1)=1; for n >= 1, a(n+1) = (n+2)*a(n) + 2*Sum_{k=2..n-1} binomial(n, k)*a(k)*a(n-k+1).
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%I #4 Mar 30 2012 16:50:26

%S 0,1,3,12,114,1404,22968,456408,10762992,292851648,9038285280,

%T 311858347968,11896746473088,497156854363776,22586083785232128,

%U 1108320770197398528,58420751739908940288,3292054745517600648192,197491129333671926863872,12566253138627465234487296

%N a(0)=0, a(1)=1; for n >= 1, a(n+1) = (n+2)*a(n) + 2*Sum_{k=2..n-1} binomial(n, k)*a(k)*a(n-k+1).

%C The recurrence for A000311, with slightly different initial conditions.

%H T. D. Noe, <a href="/A119649/b119649.txt">Table of n, a(n) for n = 0..100</a>

%p M:=50; a:=array(0..100); a[0]:=0; a[1]:=1; lprint(0,a[0]); lprint(1,a[1]); for n from 1 to M do a[n+1]:=(n+2)*a[n]+2*add(binomial(n,k)*a[k]*a[n-k+1],k=2..n-1); lprint(n+1,a[n+1]); od:

%Y Cf. A000311.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jul 30 2006