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

0,4

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.

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]]

Crossrefs

Cf. A238132.

Sequence in context: A005186 A259881 A238132 * A332305 A340282 A008642

Adjacent sequences: A278293 A278294 A278295 * A278297 A278298 A278299

Keyword

nonn

Author

Vladimir Reshetnikov, Nov 16 2016

Status

approved