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A292137 G.f.: Im(1/(i*x; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1). 7
0, 1, 1, 0, 0, 0, -1, -2, -2, -2, -2, -3, -3, -2, -2, -2, -1, 1, 2, 2, 4, 6, 7, 8, 10, 13, 14, 14, 15, 17, 17, 15, 15, 16, 14, 10, 8, 6, 1, -5, -10, -14, -21, -31, -38, -43, -53, -64, -71, -77, -86, -97, -104, -108, -115, -124, -127, -125, -127, -130, -125, -116 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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

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

FORMULA

1/(i*x; x)_inf is the g.f. for A292136(n) + i*a(n).

a(n) = Sum (-1)^((k - 1)/2) where the sum is over all integer partitions of n into an odd number of parts and k is the number of parts. - Gus Wiseman, Mar 08 2018

EXAMPLE

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

MATHEMATICA

Im[CoefficientList[Series[1/QPochhammer[I*x, x], {x, 0, 100}], x]] (* Vaclav Kotesovec, Sep 17 2017 *)

CROSSREFS

Cf. A000108, A010815, A027193, A063834, A067659, A081362, A099323, A196545, A220418, A290261, A292042, A292043, A292136, A292138, A298118, A300355.

Sequence in context: A323246 A185617 A250268 * A292138 A322665 A273632

Adjacent sequences:  A292134 A292135 A292136 * A292138 A292139 A292140

KEYWORD

sign,look

AUTHOR

Seiichi Manyama, Sep 09 2017

STATUS

approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)