Search: id:A145557 Results 1-1 of 1 results found. %I A145557 %S A145557 1,5,13,361,31,1193,31021,34467,5273479,1821745,220211,230450795,2880634987, %T A145557 1502939987,5896829249,12430516053889,1381168450513,3271188435379,2299645470079393, %U A145557 459929094015491,819873602375609,810854992749436603,311867304903633289 %N A145557 Numerators of partial sums of a certain alternating series of inverse central binomial coefficients. %C A145557 See A145558 for the denominators divided by 2. %C A145557 The limit of the rational partial sums r(n), defined below, for n->infinity is 2*(2*phi-1)*ln(phi)/5, with phi:=(1+sqrt(5))/2 (golden section). This limit is approximately 0.4304089412. %D A145557 C. Elsner, On recurrence formulae for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45. Eq.12, p.39. %D A145557 A. J. van der Poorten, Some wonderful formulae...Footnote to Apery's proof of the irrationality of zeta(3), S\'eminaire Delange-Pisot-Poitou. Th\'eorie des nombres, tome 20, no 2 (1978-1979), exp, no 29, p.1-7. p. 29-02 Available via http://www.numdam.org/numdam-bin/qrech %D A145557 R. Sprugnoli, Sums of reciprocals of the central binomial coefficients, Integers: electronic journal of combinatorial number theory, 6 (2006) #A27, 1-18. %H A145557 W. Lang, Rationals and more. %F A145557 a(n)=numerator(r(n)) with the rationals (in lowest terms) r(n):=sum(((-1)^(k+1))/ (k*binomial(2*k,k)),k=1..n). %e A145557 Rationals r(n) (in lowest terms): [1/2, 5/12, 13/30, 361/840, 31/72, 1193/2772, 31021/72072,...]. %Y A145557 A145375/A145556. %Y A145557 Sequence in context: A085554 A067135 A122900 this_sequence A012033 A007540 A157250 %Y A145557 Adjacent sequences: A145554 A145555 A145556 this_sequence A145558 A145559 A145560 %K A145557 nonn,frac,easy %O A145557 1,2 %A A145557 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 17 2008 Search completed in 0.001 seconds