A278402 G.f.: Im(2/(i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

1, 1, 0, -1, -1, -1, -3, -3, -2, -2, -2, -2, -1, 1, 1, 2, 5, 7, 7, 8, 11, 12, 12, 13, 15, 16, 14, 12, 12, 11, 6, 2, 1, -3, -10, -17, -21, -27, -37, -45, -50, -57, -68, -77, -81, -86, -96, -102, -101, -103, -108, -109, -103, -97, -95, -88, -71, -54, -42, -24, 5

Offset: 0

Author

Vladimir Reshetnikov, Nov 20 2016

Keywords

• sign

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, A278401.

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 09 2021

Mathematica

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

Formula

2/(i; x)_inf is the g.f. for A278401(n) + i*a(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 09 2021