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A278402 G.f.: Im(2/(i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

%I A278402 #13 Feb 16 2025 08:33:37
%S A278402 1,1,0,-1,-1,-1,-3,-3,-2,-2,-2,-2,-1,1,1,2,5,7,7,8,11,12,12,13,15,16,
%T A278402 14,12,12,11,6,2,1,-3,-10,-17,-21,-27,-37,-45,-50,-57,-68,-77,-81,-86,
%U A278402 -96,-102,-101,-103,-108,-109,-103,-97,-95,-88,-71,-54,-42,-24,5
%N A278402 G.f.: Im(2/(i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).
%C A278402 The q-Pochhammer symbol (a; q)_inf = Product_{k>=0} (1 - a*q^k).
%H A278402 Seiichi Manyama, <a href="/A278402/b278402.txt">Table of n, a(n) for n = 0..1000</a>
%H A278402 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A278402 2/(i; x)_inf is the g.f. for A278401(n) + i*a(n).
%F A278402 G.f.: Sum_{n >= 0} (-1)^n*x^(2*n)*(1 + x - x^(2*n+1))/Product_{k = 1..2*n+1} (1 - x^k). - _Peter Bala_, Feb 09 2021
%p A278402 with(gfun): series( add( (-1)^n*x^(2*n)*(1 + x - x^(2*n+1))/mul(1 - x^k, k = 1..2*n+1), n = 0..50), x, 101): seriestolist(%); # _Peter Bala_, Feb 09 2021
%t A278402 Im[(2/QPochhammer[I, x] + O[x]^70)[[3]]]
%Y A278402 Cf. A278399, A278400, A278401.
%K A278402 sign
%O A278402 0,7
%A A278402 _Vladimir Reshetnikov_, Nov 20 2016