A208733 Sequence related to Kashaev's invariant for the (5,2)-torus knot.
1, 2, 6, 23, 109, 621, 4149, 31851, 276408, 2676388, 28608866, 334647768, 4252140022, 58322409086, 858871301034
Offset: 0
Links
- K. Hikami, Volume Conjecture and Asymptotic Expansion of q-Series, Experimental Mathematics Vol. 12, Issue 3 (2003).
Formula
Define F(q) := sum {m,n >= 0} (q^(-m*n)*product {i = 1.. m+n} (1-q^i)).O.g.f.: F(1-q) = 1 + 2*q + 6*q^2 + 23*q^3 + ....
For n >=1, a(n) = 1/n!*sum {k = 1..n} |Stirling1(n,k)|*A208730(k).
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