A292052 - OEIS

%I #25 Sep 09 2017 03:20:19

%S 0,1,1,1,1,1,0,0,-1,-2,-3,-4,-6,-7,-9,-10,-12,-13,-15,-15,-16,-16,-16,

%T -14,-13,-9,-6,0,5,14,22,34,45,60,74,93,110,132,152,177,199,226,249,

%U 277,300,328,348,373,389,408,417,428,425,424,407,389,352,314,252

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

%H Robert Israel, <a href="/A292052/b292052.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.

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

%F a(n) = -A292043(n).

%e 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 + ...

%p N:= 100: # to get a(0)..a(N)

%p P:= mul(1+I*x^k, k=1..N):

%p S:= series(P, x, N+1):

%p seq(evalc(Im(coeff(S,x,j))),j=0..N); # _Robert Israel_, Sep 08 2017

%t Im[CoefficientList[Series[QPochhammer[-I*x, x], {x, 0, 100}], x]] (* _Vaclav Kotesovec_, Sep 09 2017 *)

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

%K sign,look

%O 0,10

%A _Seiichi Manyama_, Sep 08 2017