A278298 Expansion of ((sqrt(2);x)_inf + (-sqrt(2);x)_inf - 2)/4, where(a;q)_inf is the q-Pochhammer symbol.
1, 1, 2, 2, 3, 5, 6, 8, 11, 15, 18, 24, 29, 37, 48, 58, 71, 89, 108, 132, 163, 195, 236, 284, 341, 405, 486, 578, 683, 809, 954, 1120, 1319, 1543, 1806, 2112, 2457, 2857, 3320, 3850, 4451, 5149, 5936, 6840, 7879, 9047, 10376, 11900, 13613, 15561, 17770, 20266
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
- Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.
Programs
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Mathematica
((QPochhammer[Sqrt[2], x] + QPochhammer[-Sqrt[2], x] - 2)/4 + O[x]^53)[[3]]
Formula
a(n) ~ sqrt(1 + sqrt(2)) * c^(1/4) * exp(2*sqrt(c*n)) / (8*sqrt(Pi)*n^(3/4)), where c = Pi^2/6 + log(2)^2/8 + polylog(2, -1/sqrt(2)) = 1.0944511783086747574574059... - Vaclav Kotesovec, Oct 11 2018
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