login
Row 6 of table A113143; equal to INVERT of 6-fold factorials shifted one place right.
1

%I #8 Sep 08 2013 13:30:50

%S 1,1,2,10,110,1954,47270,1437562,52531310,2239259266,109021857446,

%T 5966767051354,362558298692270,24214789406313442,1763062297639690790,

%U 138975554045857840570,11790733617760291994990,1071215297856049456744642

%N Row 6 of table A113143; equal to INVERT of 6-fold factorials shifted one place right.

%F a(n) = Sum_{j=0..k} 6^(k-j)*A111146(k, j).

%F a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A008542(n-k).

%e A(x) = 1 + x + 2*x^2 + 10*x^3 + 110*x^4 + 1954*x^5 +...

%e = 1/(1 - x - x^2 - 7*x^3 - 91*x^4 -...- A008542(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,6*i+1)));return(polcoeff(A,n,X))}

%Y Cf. A113143, A008542 (6-fold factorials).

%K nonn

%O 0,3

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