A120016 - OEIS

%I #5 Aug 24 2017 22:41:48

%S 1,1,3,15,106,982,11383,159595,2636590,50278058,1088631886,

%T 26409797526,710034913212,20963748887980,674521750652735,

%U 23497037813799795,881180319357526102,35400836754598975554,1516991897621421273210

%N a(n) = A120014(n)/n = coefficient of x^n, divided by n, in the n-th iteration of the g.f. of A120009 for n>=1.

%F a(n) = [x^n] (x/n)*((1-n+n^2) - n^2*(n+1)*x - n*(1-(n+2)*x)*C(x) )/(1-n+n^2*x)^2, where C(x) = (1-sqrt(1-4*x))/(2*x) is the Catalan function (A000108).

%o (PARI) {a(n)=local(k=n,x=X+X^3*O(X^n));(1/n)*polcoeff( x*((1-k+k^2)-k^2*(k+1)*x-k*(1-(k+2)*x)*(1-sqrt(1-4*x))/2/x)/(1-k+k^2*x)^2,n,X)}

%Y Cf. A120009, A120014, A120022; A000108.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jun 07 2006