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

%I A292052 #26 Feb 16 2025 08:33:51
%S A292052 0,1,1,1,1,1,0,0,-1,-2,-3,-4,-6,-7,-9,-10,-12,-13,-15,-15,-16,-16,-16,
%T A292052 -14,-13,-9,-6,0,5,14,22,34,45,60,74,93,110,132,152,177,199,226,249,
%U A292052 277,300,328,348,373,389,408,417,428,425,424,407,389,352,314,252
%N A292052 G.f.: Im((-i*x; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).
%H A292052 Robert Israel, <a href="/A292052/b292052.txt">Table of n, a(n) for n = 0..10000</a>
%H A292052 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A292052 (-i*x; x)_inf is the g.f. for A292042(n) + i*a(n).
%F A292052 a(n) = -A292043(n).
%e A292052 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 A292052 N:= 100: # to get a(0)..a(N)
%p A292052 P:= mul(1+I*x^k, k=1..N):
%p A292052 S:= series(P, x, N+1):
%p A292052 seq(evalc(Im(coeff(S,x,j))),j=0..N); # _Robert Israel_, Sep 08 2017
%t A292052 Im[CoefficientList[Series[QPochhammer[-I*x, x], {x, 0, 100}], x]] (* _Vaclav Kotesovec_, Sep 09 2017 *)
%Y A292052 Cf. A278399, A278400, A278420, A292042, A292043.
%K A292052 sign,look
%O A292052 0,10
%A A292052 _Seiichi Manyama_, Sep 08 2017