A276475 a(n) = ((sqrt(2); sqrt(2))_n - (-sqrt(2); -sqrt(2))_n)/(2*sqrt(2)), where (q; q)_n is the q-Pochhammer symbol.

0, -1, 1, 3, -9, -69, 483, 5355, -80325, -2081205, 64517355, 2738408715, -172519749045, -17158004483445, 2179066569397515, 365466952872801675, -93194072982564427125, -36694334101466364023925, 18750804725849312016225675

Offset: 0

Author

Vladimir Reshetnikov, Sep 12 2016

Keywords

• sign

Comments

The q-Pochhammer symbol (q; q)n = Product{k=1..n} (1 - q^k).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..114
• Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Crossrefs

Cf. A276474, A263687, A263688.

Programs

Mathematica

Round@Table[(QPochhammer[Sqrt[2], Sqrt[2], n] - QPochhammer[-Sqrt[2], -Sqrt[2], n])/(2 Sqrt[2]), {n, 0, 20}]

Formula

(sqrt(2); sqrt(2))_n = A276474(n) + a(n)*sqrt(2).

(-sqrt(2); -sqrt(2))_n = A276474(n) - a(n)*sqrt(2).