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%I #11 Sep 08 2013 13:30:50
%S 1,1,2,7,41,364,4409,67573,1248626,26948347,664414997,18409263772,
%T 566018365445,19117946453041,703533848468330,28013710891743007,
%U 1199943043040160401,55013996422974758476,2687888298887895948065,139414898768304344206141
%N Row 3 of table A113143; equal to INVERT of triple (or 3-fold) factorials shifted one place right.
%F a(n) = Sum_{j=0..k} 3^(k-j)*A111146(k, j).
%F a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A007559(n-k).
%F G.f.: 1/(Q(0)-x) where Q(k) = 1 - x*(3*k+1)/( 1 - x*(3*k+3)/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Mar 21 2013
%e A(x) = 1 + x + 2*x^2 + 7*x^3 + 41*x^4 + 364*x^5 + 4409*x^6
%e +...
%e = 1/(1 - x - x^2 - 4*x^3 - 28*x^4 -...- A007559(n)*x^(n+1)
%e -...).
%o (PARI) {a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0,n,x^j*prod(i=0,j,3*i+1)));return(polcoeff(A,n,X))}
%Y Cf. A113143, A007559 (3-fold factorials).
%K nonn
%O 0,3
%A _Philippe Deléham_ and _Paul D. Hanna_, Oct 28 2005
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