%I #14 Aug 20 2018 07:53:18

%S 1,0,0,2,2,4,4,6,6,8,12,14,18,24,32,38,50,60,76,90,110,136,164,194,

%T 234,280,336,402,474,564,668,790,926,1096,1276,1494,1754,2040,2368,

%U 2758,3186,3692,4268,4922,5670,6528,7492,8594,9858,11272,12888,14722,16786

%N Expansion of ((sqrt(2)-1)*(-sqrt(2);x)_inf - (sqrt(2)+1)*(sqrt(2);x)_inf)/2, where (a;q)_inf is the q-Pochhammer symbol.

%C The q-Pochhammer symbol (a;q)_inf = Product_{k>=0} (1 - a*q^k).

%C a(n) agrees with A238132(n) for 0 < n < 21.

%H G. C. Greubel, <a href="/A278296/b278296.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.

%p qP := (x,y) -> (y-1)*QDifferenceEquations:-QPochhammer(-y,x,99):

%p dP := x -> (qP(x,sqrt(2)) + qP(x,-sqrt(2)))/2:

%p simplify(expand(dP(x),x)): seq(coeff(%,x,n), n=0..52); # _Peter Luschny_, Nov 17 2016

%t Simplify@(((Sqrt[2] - 1) QPochhammer[-Sqrt[2], x] - (Sqrt[2] + 1) QPochhammer[Sqrt[2], x])/2 + O[x]^53)[[3]]

%Y Cf. A238132.

%K nonn

%O 0,4

%A _Vladimir Reshetnikov_, Nov 16 2016