A278399 G.f.: Re((i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

1, -1, -1, -2, -2, -3, -2, -3, -2, -2, 0, 0, 3, 4, 8, 9, 14, 16, 22, 24, 30, 32, 39, 40, 46, 46, 51, 48, 52, 46, 46, 36, 32, 16, 8, -15, -30, -60, -82, -122, -151, -200, -238, -296, -342, -412, -464, -542, -602, -686, -750, -841, -904, -996, -1058, -1146, -1198

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. A278400, A278401, A278402, A278420, A292042, A292043.

Programs

Maple

G := add((-1)^n*x^(n*(2*n-1))/mul(1 - x^k, k = 1..2*n), n = 0..7):
S := series(G, x, 101):
seq(coeff(S, x, j), j = 0..100); # Peter Bala, Feb 04 2021

Mathematica

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

Formula

(i; x)_inf is the g.f. for a(n) + i*A278400(n).

G.f.: Sum_{n >= 0} (-1)^n^x^(n*(2*n-1))/Product_{k = 1..2*n} 1 - x^k. - Peter Bala, Feb 04 2021