This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A121008 Numerators of partial alternating sums of Catalan numbers scaled by powers of 1/(5*3^2) = 1/45. 6
 1, 44, 1982, 17837, 4013339, 60200071, 2709003239, 121905145612, 658287786362, 740573759652388, 33325819184374256, 1499661863296782734, 67484783848355431042, 607363054635198730798, 3036815273175993713422 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Denominators are given under A121009. This is the second member (p=2) of the third p-family of partial sums of normalized scaled Catalan series CsnIII(p):=sum(((-1)^k)*C(k)/((5^k)*F(2*p)^(2*k)),k=0..infinity) with limit F(2*p)*(-L(2*p+1) + L(2*p)*phi) = F(2*p)*sqrt(5)/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 third p-family are rIII(p;n):=sum(((-1)^k)*C(k)/((5^k)*F(2*p)^(2*k)),k=0..n), n>=0, for p=1,... For more details on this p-family and the other three ones see the W. Lang link under A120996. LINKS W. Lang: Rationals r(n), limit. FORMULA a(n)=numerator(r(n)) with r(n) := rIII(p=2,n) = sum(((-1)^k)*C(k)/((5^k)*F(2*2)^(2*k)),k=0..n), with F(4)=3 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms. EXAMPLE Rationals r(n): [1, 44/45, 1982/2025, 17837/18225, 4013339/4100625, 60200071/61509375, 2709003239/2767921875,...]. MAPLE The limit lim_{n->infinity}(r(n) := rIII(2; n)) = 3*(-11 + 7*phi) = 3*sqrt(5)/phi^4 = 0.9787137637479 (maple10, 15 digits). CROSSREFS The first member (p=1) is A121006/A121007. Sequence in context: A009988 A041925 A094506 * A250446 A233941 A271137 Adjacent sequences:  A121005 A121006 A121007 * A121009 A121010 A121011 KEYWORD nonn,frac,easy AUTHOR Wolfdieter Lang, Aug 16 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)