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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 09:20 EDT 2022. Contains 353741 sequences. (Running on oeis4.)