A208731 Sequence related to Kashaev's invariant for the (7,2)-torus knot.

1, 3, 21, 303, 7581, 291903, 16004541, 11842303, 113649275901, 13729560793503, 2038432934681661, 364819653173167503, 77453921498088781821, 19245815560568454066303, 5532998260944453966936381

Offset: 0

Author

Peter Bala, Mar 01 2012

Keywords

• nonn
• easy

Comments

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

Links

• K. Hikami, Volume Conjecture and Asymptotic Expansion of q-Series, Experimental Mathematics Vol. 12, Issue 3 (2003).

Crossrefs

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

Formula

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

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- ....