A208735 -id:A208735 - cp's OEIS frontend

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

Peter Bala, Mar 01 2012

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

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

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

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- ....

A208734 Sequence related to Kashaev's invariant for the (7,2)-torus knot.

Original entry on oeis.org

1, 3, 12, 62, 402, 3162, 29308, 312975, 3784365, 51110995, 762628152, 12458953182, 221186147507, 4240110073077, 87290431614432

Offset: 0

Peter Bala, Mar 02 2012

This is sequence a_n(7) in Table 3 of Hikami 2003.

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

Cf. A208680, A208731, A208733, A208735.

For n >=1, a(n) = 1/n!*sum {k = 1..n} |Stirling1(n,k)|*A208731(k).

cp's OEIS Frontend

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

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