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A120792
Numerators of partial sums of Catalan numbers scaled by powers of -1/12.
2
1, 11, 67, 1603, 9625, 4277, 230969, 11086369, 199555357, 2394661853, 14367975317, 344831378215, 2068988321293, 24827859669791, 49655719451017, 1588983021355339, 9533898130096349, 343220332661861099
OFFSET
0,2
COMMENTS
Denominators are given under A120793.
From the expansion of sqrt(1+1/3) = 1+(1/6)*Sum_{k=0..oo} C(k)/(-12)^k one has, with the partial sums r(n) are defined below, r := lim_{n->oo} r(n) = 2*(2*sqrt(3)-3) = 0.9282032302....
FORMULA
a(n)=numerator(r(n)), with the rationals r(n):=Sum_{k=0..n} ((-1)^k)*C(k)/12^k with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.
EXAMPLE
Rationals r(n): [1, 11/12, 67/72, 1603/1728, 9625/10368, 4277/4608, 230969/248832, 11086369/11943936, 199555357/214990848,...].
CROSSREFS
Sequence in context: A165673 A220511 A287169 * A228032 A145833 A111931
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Jul 20 2006
STATUS
approved