A120016 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.

1, 1, 3, 15, 106, 982, 11383, 159595, 2636590, 50278058, 1088631886, 26409797526, 710034913212, 20963748887980, 674521750652735, 23497037813799795, 881180319357526102, 35400836754598975554, 1516991897621421273210

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

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).

Prog

(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)}

Crossrefs

Cf. A120009, A120014, A120022; A000108.

Sequence in context: A295124 A107878 A218688 * A349874 A074519 A105618

Adjacent sequences: A120013 A120014 A120015 * A120017 A120018 A120019

Keyword

nonn

Author

Paul D. Hanna, Jun 07 2006

Status

approved