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A278298 Expansion of ((sqrt(2);x)_inf + (-sqrt(2);x)_inf - 2)/4, where(a;q)_inf is the q-Pochhammer symbol.

%I A278298 #13 Feb 16 2025 08:33:37
%S A278298 1,1,2,2,3,5,6,8,11,15,18,24,29,37,48,58,71,89,108,132,163,195,236,
%T A278298 284,341,405,486,578,683,809,954,1120,1319,1543,1806,2112,2457,2857,
%U A278298 3320,3850,4451,5149,5936,6840,7879,9047,10376,11900,13613,15561,17770,20266
%N A278298 Expansion of ((sqrt(2);x)_inf + (-sqrt(2);x)_inf - 2)/4, where(a;q)_inf is the q-Pochhammer symbol.
%C A278298 The q-Pochhammer symbol (a;q)_inf = Product_{k>=0} (1 - a*q^k).
%C A278298 a(n) agrees with A118399(n) for n < 15.
%H A278298 G. C. Greubel, <a href="/A278298/b278298.txt">Table of n, a(n) for n = 1..5000</a>
%H A278298 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A278298 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
%t A278298 ((QPochhammer[Sqrt[2], x] + QPochhammer[-Sqrt[2], x] - 2)/4 + O[x]^53)[[3]]
%Y A278298 Cf. A118399, A278296.
%K A278298 nonn
%O A278298 1,3
%A A278298 _Vladimir Reshetnikov_, Nov 17 2016