

A121003


Denominators of partial sums of Catalan numbers scaled by powers of 1/5.


1



1, 5, 25, 25, 625, 3125, 15625, 78125, 3125, 1953125, 9765625, 48828125, 244140625, 244140625, 1220703125, 6103515625, 30517578125, 152587890625, 152587890625, 3814697265625, 19073486328125
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OFFSET

0,2


COMMENTS

Numerators are given under A121002.
This is the first member (p=0) of the second pfamily 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+1)*sqrt(5)/phi^(2*p+1), with C(n)=A000108(n) (Catalan), F(n)= A000045(n) (Fibonacci), L(n) = A000032(n) (Lucas) and phi:=(1+sqrt(5))/2 (golden section).
For more details on this pfamily and the other three ones see the W. Lang links under A120996 and A121002.


LINKS

Table of n, a(n) for n=0..20.


FORMULA

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


EXAMPLE

Rationals r(n): [1, 6/5, 32/25, 33/25, 839/625, 4237/3125,
21317/15625, 107014/78125, 4292/3125, 2687362/1953125,...].
A120787 (denominators, second member p=1).


CROSSREFS

Sequence in context: A265928 A039936 A124398 * A121007 A043057 A137112
Adjacent sequences: A121000 A121001 A121002 * A121004 A121005 A121006


KEYWORD

nonn,frac,easy


AUTHOR

Wolfdieter Lang, Aug 16 2006


STATUS

approved



