A121005 Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/125.

1, 125, 15625, 390625, 244140625, 30517578125, 3814697265625, 476837158203125, 11920928955078125, 7450580596923828125, 931322574615478515625, 116415321826934814453125, 14551915228366851806640625

Offset

0,2

Comments

This is the third member (p=2) of the second p-family of partial sums of normalized scaled Catalan series CsnII(p):=sum(C(k)/((5^k)*F(2*p+1)^(2*k)),k=0..infinity) with limit F(2*p+1)*(L(2*p+2) - L(2*p+1)*phi) = F(2*p)*sqrt(5)/phi^(2*p), with 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 second p-family are rII(p;n):=sum(C(k)/((5^k)*F(2*p+1)^(2*k)),k=0..n), n>=0, for p=0,1,...

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

Numerators are given under A121004.

Links

Table of n, a(n) for n=0..12.

Formula

a(n)=denominator(r(n)) with r(n) := rII(p=2,n) = sum(C(k)/5^(3*k),k=0..n) and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.

Example

Rationals r(n): [1, 126/125, 15752/15625, 393801/390625,
246125639/244140625, 30765704917/30517578125,...].

Crossrefs

Sequence in context: A347510 A275296 A259925 * A264062 A067972 A094197

Adjacent sequences: A121002 A121003 A121004 * A121006 A121007 A121008

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Aug 16 2006

Status

approved