A278400 G.f.: Im((i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

-1, -1, -1, 0, 0, 1, 2, 3, 4, 6, 6, 8, 9, 10, 10, 11, 10, 10, 8, 6, 2, 0, -7, -12, -20, -28, -39, -48, -62, -74, -90, -104, -122, -136, -156, -171, -190, -204, -222, -232, -247, -252, -260, -258, -258, -244, -232, -204, -176, -130, -84, -15, 54, 148, 244, 368

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..10000
• Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Crossrefs

Cf. A278399, A278401, A278402, A278420, A292042, A292043.

Programs

Maple

with(gfun): series(add((-1)^(n+1)*x^(n*(2*n+1))/mul(1 - x^k, k = 1..2*n+1), n = 0..6), x, 100): seriestolist(%); # Peter Bala, Feb 06 2021

Mathematica

Im[(QPochhammer[I, x] + O[x]^60)[[3]]]

Formula

(i; x)_inf is the g.f. for A278399(n) + i*a(n).

G.f.: Sum_{n >= 0} (-1)^(n+1)*x^(n*(2*n+1))/Product_{k = 1..2*n+1} 1 - x^k. - Peter Bala, Feb 06 2021