A292042 G.f.: Re((i*x; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

1, 0, 0, -1, -1, -2, -2, -3, -3, -4, -3, -4, -3, -3, -1, -1, 2, 3, 7, 9, 14, 16, 23, 26, 33, 37, 45, 48, 57, 60, 68, 70, 77, 76, 82, 78, 80, 72, 70, 55, 48, 26, 11, -19, -42, -84, -116, -169, -213, -278, -333, -413, -479, -572, -651, -757, -846, -965, -1062

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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

Formula

( i*x; x)_inf is the g.f. for a(n) + i*A292043(n).

(-i*x; x)_inf is the g.f. for a(n) + i*A292052(n).

a(n)^2 + A292043(n)^2 = A278420(n). - Vaclav Kotesovec, Sep 08 2017

From Peter Bala, Jan 15 2021: (Start)

G.f.: A(x) = Sum_{n >= 0} (-1)^n*x^(n*(2*n+1))/Product_{k = 1..2*n} (1 - x^k). Cf. A035294.

Conjectural g.f.: A(x) = (1/2)*Sum_{n >= 0} (-x)^(n*(n-1)/2)/Product_{k = 1..n} (1 - x^k). (End)

Example

Product_{k>=1} (1 - i*x^k) = 1 + (0-1i)*x + (0-1i)*x^2 + (-1-1i)*x^3 + (-1-1i)*x^4 + (-2-1i)*x^5 + (-2+0i)*x^6 + (-3+0i)*x^7 + ...

Maple

N:= 100:
S := convert(series( add( (-1)^n*x^(n*(2*n+1))/(mul(1 - x^k, k = 1..2*n)), n = 0..floor(sqrt(N/2)) ), x, N+1 ), polynom):
seq(coeff(S, x, n), n = 0..N); # Peter Bala, Jan 15 2021

Mathematica

Re[CoefficientList[Series[QPochhammer[I*x, x], {x, 0, 100}], x]] (* Vaclav Kotesovec, Sep 08 2017 *)

Crossrefs

Cf. A035294, A278399, A278400, A278420, A292043, A292052.

Sequence in context: A332894 A269989 A057935 * A282715 A124831 A105096

Adjacent sequences: A292039 A292040 A292041 * A292043 A292044 A292045

Keyword

sign

Author

Seiichi Manyama, Sep 08 2017

Status

approved