A113145 - OEIS

%I #11 Sep 08 2013 13:30:50

%S 1,1,2,8,60,708,11428,232756,5704964,163192820,5331728964,

%T 195776203764,7978838333188,357313060904692,17438518614448580,

%U 921145685670017012,52355425184381107332,3185815887918686343924,206633438251087758833476

%N Row 4 of table A113143; equal to INVERT of quartic (or 4-fold) factorials shifted one place right.

%F a(n) = Sum_{j=0..k} 4^(k-j)*A111146(k, j).

%F a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A007696(n-k).

%F G.f.: 1/(T(0) - x) where T(k) =  1 - x*(4*k+1)/(1 - x*(4*k+4)/T(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Mar 19 2013

%e A(x) = 1 + x + 2*x^2 + 8*x^3 + 60*x^4 + 708*x^5 +...

%e = 1/(1 - x - x^2 - 5*x^3 - 45*x^4 -...- A007696(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,4*i+1)));return(polcoeff(A,n,X))}

%Y Cf. A113143, A007696 (4-fold factorials).

%K nonn

%O 0,3

%A _Philippe Deléham_ and _Paul D. Hanna_, Oct 28 2005