A292052 G.f.: Im((-i*x; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

0, 1, 1, 1, 1, 1, 0, 0, -1, -2, -3, -4, -6, -7, -9, -10, -12, -13, -15, -15, -16, -16, -16, -14, -13, -9, -6, 0, 5, 14, 22, 34, 45, 60, 74, 93, 110, 132, 152, 177, 199, 226, 249, 277, 300, 328, 348, 373, 389, 408, 417, 428, 425, 424, 407, 389, 352, 314, 252

Offset

0,10

Links

Robert Israel, Table of n, a(n) for n = 0..10000

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

Formula

(-i*x; x)_inf is the g.f. for A292042(n) + i*a(n).

a(n) = -A292043(n).

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: # to get a(0)..a(N)
P:= mul(1+I*x^k, k=1..N):
S:= series(P, x, N+1):
seq(evalc(Im(coeff(S, x, j))), j=0..N); # Robert Israel, Sep 08 2017

Mathematica

Im[CoefficientList[Series[QPochhammer[-I*x, x], {x, 0, 100}], x]] (* Vaclav Kotesovec, Sep 09 2017 *)

Crossrefs

Cf. A278399, A278400, A278420, A292042, A292043.

Sequence in context: A230748 A078607 A292043 * A347624 A187484 A186237

Adjacent sequences: A292049 A292050 A292051 * A292053 A292054 A292055

Keyword

sign,look

Author

Seiichi Manyama, Sep 08 2017

Status

approved