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A278400 G.f.: Im((i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

%I A278400 #21 Feb 16 2025 08:33:37
%S A278400 -1,-1,-1,0,0,1,2,3,4,6,6,8,9,10,10,11,10,10,8,6,2,0,-7,-12,-20,-28,
%T A278400 -39,-48,-62,-74,-90,-104,-122,-136,-156,-171,-190,-204,-222,-232,
%U A278400 -247,-252,-260,-258,-258,-244,-232,-204,-176,-130,-84,-15,54,148,244,368
%N A278400 G.f.: Im((i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).
%C A278400 The q-Pochhammer symbol (a; q)_inf = Product_{k>=0} (1 - a*q^k).
%H A278400 Seiichi Manyama, <a href="/A278400/b278400.txt">Table of n, a(n) for n = 0..10000</a>
%H A278400 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A278400 (i; x)_inf is the g.f. for A278399(n) + i*a(n).
%F A278400 G.f.: Sum_{n >= 0} (-1)^(n+1)*x^(n*(2*n+1))/Product_{k = 1..2*n+1} 1 - x^k. - _Peter Bala_, Feb 06 2021
%p A278400 with(gfun): series(add((-1)^(n+1)*x^(n*(2*n+1))/mul(1 - x^k, k = 1..2*n+1), n = 0..6), x, 100): seriestolist(%); # _Peter Bala_, Feb 06 2021
%t A278400 Im[(QPochhammer[I, x] + O[x]^60)[[3]]]
%Y A278400 Cf. A278399, A278401, A278402, A278420, A292042, A292043.
%K A278400 sign,easy
%O A278400 0,7
%A A278400 _Vladimir Reshetnikov_, Nov 20 2016