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A120998 Numerators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49. 3
1, 50, 2452, 120153, 841073, 41212583, 14135916101, 692659889378, 33940334580952, 1663076394471510, 81490743329120786, 570435203303853900, 27951324961888870816, 9587304461927883432788, 469777918634466290881052 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Denominators are given under A120999.

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

The limit lim_{n->infinity} r(n) = 7*(5 - 3* phi) = 7/phi^4 = 1.0212862362522 (maple10, 15 digits).

LINKS

Table of n, a(n) for n=0..14.

W. Lang: Rationals r(n), limit.

FORMULA

a(n)=numerator(r(n)) with r(n) := rI(p=2,n) = sum(C(k)/L(4)^(2*k),k=0..n), with Lucas L(4)=7 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.

EXAMPLE

Rationals r(n): [1, 50/49, 2452/2401, 120153/117649, 841073/823543,

41212583/40353607, 14135916101/13841287201,...].

CROSSREFS

Sequence in context: A170731 A170769 A218753 * A267061 A223191 A223807

Adjacent sequences:  A120995 A120996 A120997 * A120999 A121000 A121001

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang, Aug 16 2006

STATUS

approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)