A276474 a(n) = ((sqrt(2); sqrt(2))_n + (-sqrt(2); -sqrt(2))_n)/2, where (q; q)_n is the q-Pochhammer symbol.

1, 1, -1, -5, 15, 87, -609, -8337, 125055, 2695455, -83559105, -4212669825, 265398198975, 22347926076735, -2838186611745345, -560679228377509185, 142973203236264842175, 47858338570309251530175, -24455611009428027531919425, -19225279650279123532147010625

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. A276475, A263687, A263688.

Programs

Mathematica

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

Formula

(sqrt(2); sqrt(2))_n = a(n) + A276475(n)*sqrt(2).

(-sqrt(2); -sqrt(2))_n = a(n) - A276475(n)*sqrt(2).