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%I #15 Jan 28 2013 13:21:30
%S 1,2,10,104,1870,51632,2027470,107354144,7370645950,636754087472,
%T 67591284235630,8647294709864384,1312197219579059230,
%U 233025643830843282512
%N Sequence related to Kashaev's invariant for the (5,2)-torus knot.
%C This is sequence b_n(5) 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 Define F(q) := sum {m,n >= 0} (q^(-m*n)*product {i = 1.. m+n} (1-q^i)).
%F E.g.f.: F(exp(-t)) = 1 + 2*t + 10*t^2! + 104*t^3/3! + .... For the expansion of F(1-q) see A208733. F(q) also appears in a conjectural e.g.f. for A208679.
%F a(n) = (9/40)^n*sum {k = 0..n} binomial(n,k)*A208679(k+1)/9^k.
%F Conjectural S-fraction for the o.g.f.: 1/(1-2*x/(1-3*x/(1-9*x/(1-11*x/(1-...-1/2*n*(5*n-1)*x/(1-1/2*n*(5*n+1)*x/(1- ....
%Y Cf. A079144, A208679, A208731, A208732, A208733.
%K nonn,easy
%O 0,2
%A _Peter Bala_, Mar 01 2012
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