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%I #6 Sep 08 2013 13:30:50
%S 1,4,32,272,2400,21792,203008,1940224,19065344,193410560,2038078464,
%T 22490167296,262429339648,3271314362368,43955391856640,
%U 640254018879488,10121874150653952,173145693892509696,3186234896556752896
%N a(n) = Sum_{k=0..n} 4^k*A111146(n,k).
%F G.f.: A(x) = 1/(1 - 4/3!*x*Sum(k>=0} (k+3)!*x^k ).
%e A(x) = (1 + 4*x + 32*x^2 + 272*x^3 + 2400*x^4 + 21792*x^5 +..)
%e = 1/(1 - 4/3!*x*(3! + 4!*x + 5!*x^2 + 6!*x^3 + 7!*x^4 +..) ).
%o (PARI) {a(n)=local(y=4,x=X+X*O(X^n)); polcoeff(1/(1 - y/(y-1)!*x*sum(k=0,n,(y-1+k)!*x^k)),n,X)}
%Y Cf. A111146, A113326, A113327 (y=2), A113328 (y=3), A113330 (y=5), A113331 (y=6).
%K nonn
%O 0,2
%A _Philippe Deléham_ and _Paul D. Hanna_, Oct 26 2005
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