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%I #8 Dec 13 2022 09:47:20
%S 1,-1,0,0,0,0,-1,1,-1,1,-1,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1,1,-1,0,1,-1,
%T 1,-2,3,-4,4,-5,7,-8,8,-9,11,-12,12,-13,15,-16,16,-17,19,-20,19,-20,
%U 22,-22,21,-21,22,-22,20,-19,20,-19,16,-14,14,-12,8,-5,3,0,-5,10,-13,17,-24,30,-34,40,-48,55,-61,68,-77,86,-93,101
%N Coefficients of a Ramanujan q-series.
%D S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 10
%F G.f.: Sum_{k>=0} (-1)^k * x^(k*(k + 1)/2) / (x^2; x^2)_n.
%e G.f. = 1 - x - x^6 + x^7 - x^8 + x^9 - x^10 + 2*x^11 - 2*x^12 + 2*x^13 - 2*x^14 + ...
%t a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ (-1)^k x^(k (k + 1)/2) / QPochhammer[ x^2, x^2, k], {k, 0, Sqrt[8 n + 1]}], {x, 0, n}]]; (* _Michael Somos_, Nov 01 2015 *)
%o (PARI) {a(n) = my(t); if( n<0, 0, t = 1 + x * O(x^n); polcoeff( sum(k=1, (sqrtint(8*n + 1) - 1)\2, t = -t * x^k / (1 - x^(2*k)) + x * O(x^n), 1), n))};
%Y Convolution with A015128 is A143184. - _Michael Somos_, Dec 13 2022
%K sign
%O 0,12
%A _Michael Somos_, Aug 13 2007