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 A120794 Numerators of partial sums of Catalan numbers scaled by powers of -1/16. 4
 1, 15, 121, 3867, 30943, 495067, 3960569, 253475987, 2027808611, 32444935345, 259559486959, 8305903553295, 66447228478363, 1063155655468083, 8505245244078969, 1088671391232413187 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From the expansion of sqrt(1+1/4) = 1+(1/8)*sum(C(k)/(-16)^k,k=0..infinity) one has, with the partial sums r(n) are defined below, r:=limit(r(n),n to infinity)= 4*(sqrt(5)-2) = 4*(2*phi-3)) = 0.944271909... Denominators coincide with the listed numbers of A120785 but may differ for higher n values. This is the first member (p=1) of the fourth famliy of scaled Catalan sums with limits in Q(sqrt(5)). See the W. Lang link under A120996. LINKS Table of n, a(n) for n=0..15. W. Lang: Rationals r(n) and limit. FORMULA a(n)=numerator(r(n)), with the rationals r(n):=sum(((-1)^k)*C(k)/16^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms. EXAMPLE Rationals r(n): [1, 15/16, 121/128, 3867/4096, 30943/32768, 495067/524288, 3960569/4194304,...]. CROSSREFS The second member (p=2) of this p-family is A121012/A121013. Sequence in context: A138424 A279267 A357602 * A264377 A038743 A181377 Adjacent sequences: A120791 A120792 A120793 * A120795 A120796 A120797 KEYWORD nonn,easy,frac AUTHOR Wolfdieter Lang, Jul 20 2006 STATUS approved

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)