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%I #6 Sep 08 2013 13:30:50
%S 1,5,50,525,5675,62650,703975,8042625,93454750,1106250125,13377432875,
%T 165950540250,2124087269375,28260204825625,394301229688750,
%U 5824314672613125,91872380184761875,1557002324898406250
%N a(n) = Sum_{k=0..n} 5^k*A111146(n,k).
%F G.f.: A(x) = 1/(1 - 5/4!*x*Sum(k>=0} (k+4)!*x^k ).
%e A(x) = (1 + 5*x + 50*x^2 + 525*x^3 + 5675*x^4 + 62650*x^5 +..)
%e = 1/(1 - 5/4!*x*(4! + 5!*x + 6!*x^2 + 7!*x^3 + 8!*x^4 +..) ).
%o (PARI) {a(n)=local(y=5,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), A113329 (y=4), A113331 (y=6).
%K nonn
%O 0,2
%A _Philippe Deléham_ and _Paul D. Hanna_, Oct 26 2005
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