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%I #18 Feb 14 2019 18:27:39
%S 1,1,11,35,95,73,-6809,-37129,-49763,-118151,3098985,18490177,
%T 135754015,476263867,-1506027797,-77594009,-9795145237,-181840242713,
%U -1625887512417,-14848078415067,-80493076445459,-304934409547939,-440055933017985,-4208587849042603,-23584916465354149,249312361064897267,2617671685008217267,17522498092619009285,100559736578029630325,519821481713769303651,1604365446162860783027
%N Odd coefficients in Sum_{n>=0} (x^(n+1) + i)^n / (1 + i*x^n)^(n+1), in which the constant term is taken to be 1.
%C a(n) = A323690(n*(n+1)).
%H Paul D. Hanna, <a href="/A323691/b323691.txt">Table of n, a(n) for n = 0..100</a>
%e The generating function of A323690 is
%e G(x) = Sum_{n>=0} (x^(n+1) + i)^n / (1 + i*x^n)^(n+1),
%e in which the constant term is taken to be 1, so that
%e G(x) = 1 + 2*x + x^2 - 8*x^3 + 18*x^5 + 11*x^6 - 16*x^7 - 44*x^8 + 36*x^10 - 12*x^11 + 35*x^12 + 112*x^13 + 56*x^14 - 144*x^15 - 260*x^16 - 88*x^17 + 48*x^18 - 20*x^19 + 95*x^20 + 504*x^21 + 636*x^22 + 288*x^23 - 578*x^24 - 1016*x^25 - 292*x^26 - 216*x^27 - 624*x^28 - 210*x^29 + 73*x^30 + ...
%e This sequence gives the odd coefficients of x^n, which occur at n = k*(k+1) for k >= 0.
%o (PARI) {A323690(n) = my(SUM = sum(m=0, n, (x^(m+1) + I +x*O(x^n))^m / (1 + I*x^m +x*O(x^n))^(m+1) ) ); polcoeff(1 + SUM - I^n/(1+I),n)}
%o {a(n) = A323690(n*(n+1))}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A323690.
%K sign
%O 0,3
%A _Paul D. Hanna_, Feb 13 2019
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