A278401 G.f.: Re(2/(i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

1, -1, -2, -1, -1, -1, -1, 1, 2, 2, 2, 4, 5, 5, 5, 6, 7, 5, 3, 4, 3, 0, -2, -3, -5, -10, -14, -16, -18, -23, -28, -28, -29, -35, -38, -37, -37, -39, -39, -35, -30, -29, -26, -15, -5, 0, 10, 26, 41, 51, 64, 85, 105, 119, 135, 160, 183, 196, 212, 236, 255, 265

Offset: 0

Author

Vladimir Reshetnikov, Nov 20 2016

Keywords

• sign
• easy

Comments

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

Links

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

Crossrefs

Cf. A278399, A278400, A278402.

Programs

Maple

with(gfun): series( add( (-1)^n*x^(2*n)*(1 - x - x^(2*n+1))/mul(1 - x^k, k = 1..2*n+1), n = 0..50), x, 101): seriestolist(%); # Peter Bala, Feb 08 2021

Mathematica

Re[(2/QPochhammer[I, x] + O[x]^70)[[3]]]

Formula

2/(i; x)_inf is the g.f. for a(n) + i*A278402(n).

G.f.: Sum_{n >= 0} (-1)^n*x^(2*n)*(1 - x - x^(2*n+1))/Product_{k = 1..2*n+1} (1 - x^k). - Peter Bala, Feb 08 2021