A120998 -id:A120998 - cp's OEIS frontend

A120999 Denominators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49.

1, 49, 2401, 117649, 823543, 40353607, 13841287201, 678223072849, 33232930569601, 1628413597910449, 79792266297612001, 558545864083284007, 27368747340080916343, 9387480337647754305649, 459986536544739960976801

Offset: 0

Wolfdieter Lang, Aug 16 2006

Numerators are given under A120998.
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).
See A120998 for more details and a W. Lang link there for the definition of four p-families of such scaled Catalan sums.

			Rationals r(n): [1, 50/49, 2452/2401, 120153/117649, 841073/823543,
41212583/40353607, 14135916101/13841287201,...].

a(n)=denominator(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.

A121001 Denominators of partial sums of Catalan numbers scaled by powers of 1/18^2 = 1/324.

Original entry on oeis.org

1, 324, 52488, 34012224, 5509980288, 595077871104, 96402615118848, 124937789194027008, 60719765548297125888, 19673204037648268787712, 3187059054099019543609344, 2065214267056164664258854912

Offset: 0

Wolfdieter Lang, Aug 16 2006

Numerators are given under A121000.
This is the fourth member (p=3) 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).
See A120998 for more details and a W. Lang link there for the definition of four p-families of such scaled Catalan sums.

			Rationals r(n): [1, 325/324, 52651/52488, 34117853/34012224, 5527092193/5509980288, 596925956851/595077871104, ...].

a(n)=denominator(r(n)) with r(n) := rI(p=3,n) = sum(C(k)/L(6)^(2*k),k=0..n), with Lucas L(6)=18 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.

cp's OEIS Frontend

A120999 Denominators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49.

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