A208732 Sequence related to Kashaev's invariant for the (9,2)-torus knot.

1, 4, 36, 664, 21276, 1050664, 73939356, 7024817944, 866058563196, 134419597387144, 25644210185987676, 5897980691609567224, 1609292585008090909116, 513950106691675965931624, 189914985024774644611299996

Offset

0,2

Comments

This is sequence b_n(9) in Table 2 of Hikami 2003.

Links

Table of n, a(n) for n=0..14.

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

Formula

a(n) = (49/72)^n*sum {k = 0..n} binomial(n,k)*A208681(k+1)/49^k.

Conjectural S-fraction for the o.g.f.: 1/(1-4*x/(1-5*x/(1-17*x/(1-19*x/(1-...-1/2*n*(9*n-1)*x/(1-1/2*n*(9*n+1)*x/(1- ....

Crossrefs

Cf. A079144, A208681, A208730, A208731, A208735.

Sequence in context: A268470 A365650 A214347 * A356616 A029989 A163887

Adjacent sequences: A208729 A208730 A208731 * A208733 A208734 A208735

Keyword

nonn,easy

Author

Peter Bala, Mar 01 2012

Status

approved