A208731 - OEIS

%I #12 Jan 28 2013 13:20:59

%S 1,3,21,303,7581,291903,16004541,11842303,113649275901,13729560793503,

%T 2038432934681661,364819653173167503,77453921498088781821,

%U 19245815560568454066303,5532998260944453966936381

%N Sequence related to Kashaev's invariant for the (7,2)-torus knot.

%C This is sequence b_n(7) in Table 2 of Hikami 2003.

%H K. Hikami, <a href="http://www.emis.de/journals/EM/expmath/volumes/12/12.3/Hikami.pdf">Volume Conjecture and Asymptotic Expansion of q-Series</a>, Experimental Mathematics Vol. 12, Issue 3 (2003).

%F a(n) = (25/56)^n*sum {k = 0..n} binomial(n,k)*A208680(k+1)/25^k.

%F Conjectural S-fraction for the o.g.f.: 1/(1-3*x/(1-4*x/(1-13*x/(1-15*x/(1-...-1/2*n*(7*n-1)*x/(1-1/2*n*(7*n+1)*x/(1- ....

%Y Cf. A079144, A208680, A208730, A208732, A208734.

%K nonn,easy

%O 0,2

%A _Peter Bala_, Mar 01 2012