A278296 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.

1, 0, 0, 2, 2, 4, 4, 6, 6, 8, 12, 14, 18, 24, 32, 38, 50, 60, 76, 90, 110, 136, 164, 194, 234, 280, 336, 402, 474, 564, 668, 790, 926, 1096, 1276, 1494, 1754, 2040, 2368, 2758, 3186, 3692, 4268, 4922, 5670, 6528, 7492, 8594, 9858, 11272, 12888, 14722, 16786

Offset: 0

Author

Vladimir Reshetnikov, Nov 16 2016

Keywords

• nonn

Comments

The q-Pochhammer symbol (a;q)inf = Product{k>=0} (1 - a*q^k).

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Crossrefs

Cf. A238132.

Programs

Maple

qP := (x,y) -> (y-1)*QDifferenceEquations:-QPochhammer(-y,x,99):
dP := x -> (qP(x,sqrt(2)) + qP(x,-sqrt(2)))/2:
simplify(expand(dP(x),x)): seq(coeff(%,x,n), n=0..52); # Peter Luschny, Nov 17 2016

Mathematica

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