A121013 Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(11^2) = 1/121.

1, 121, 14641, 1771561, 214358881, 25937424601, 285311670611, 34522712143931, 4177248169415651, 505447028499293771, 672749994932560009201, 81402749386839761113321, 9849732675807611094711841

Offset: 0

Author

Wolfdieter Lang, Aug 16 2006

Keywords

• nonn
• frac
• easy

Comments

This is the second member (p=2) of the fourth (normalized) p-family of partial sums of the normalized scaled Catalan series CsnIV(p):=sum(((-1)^k)*C(k)/L(2*p+1)^(2*k),k=0..infinity) with limit L(2*p+1)*(-F(2*p+2) + F(2*p+1)*phi) = L(2*p+1)/phi^(2*p+1), where C(n)=A000108(n) (Catalan), F(n)= A000045(n) (Fibonacci), L(n) = A000032(n) (Lucas) and phi:=(1+sqrt(5))/2 (golden section).

The partial sums of the above mentioned fourth p-family are rIV(p;n):=sum(((-1)^k)*C(k)/L(2*p+1)^(2*k),k=0..n), n>=0, for p=1,...

For more details on this p-family and the other three ones see the W. Lang links under A120996 and A121012.

Examples

			Rationals r(n): [1, 120/121, 14522/14641, 1757157/1771561, 212616011/214358881, 25726537289/25937424601,...].
		

Crossrefs

The first member is A120794/A120785. The third member is A121498/A121499.

Formula

a(n)=denominator(r(n)) with r(n) := rIV(p=2,n) = sum(((-1)^k)*C(k)/L(2*2+1)^(2*k), k=0..n), with L(5)=11 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.