cp's OEIS Frontend

A096661 Fine's numbers J(n).

%I A096661 #21 Feb 19 2021 10:43:27
%S A096661 0,0,-1,1,-1,1,-1,2,-1,0,-1,2,-1,0,-1,1,-1,0,0,2,-1,-1,-1,2,0,0,0,1,
%T A096661 -1,0,-1,2,-1,-1,0,2,0,0,-2,1,-2,0,1,2,-1,0,-2,2,0,0,-1,1,-1,0,-1,3,
%U A096661 -1,0,0,2,-1,0,-2,0,-1,1,1,2,-1,0,-3,2,0,0,0,1,-1,-1,-1,2,-2,0,0,2,1,1,-2,0,-1,0,0,1,-1,0,-2,3,0,0,1,0,-1,0,-1,2,-1
%N A096661 Fine's numbers J(n).
%D A096661 N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 62, Eq. (27.1).
%H A096661 G. C. Greubel, <a href="/A096661/b096661.txt">Table of n, a(n) for n = 0..5000</a>
%H A096661 L. A. Dragonette, <a href="http://dx.doi.org/10.1090/S0002-9947-1952-0049927-8">Some Asymptotic Formulae for the Mock Theta Series of Ramanujan</a>, Trans. Amer. Math. Soc., 72 (1952), 474-500. See page 496.
%F A096661 G.f.: Sum_{n >= 1} (-1)^n*q^((3*n^2+n)/2)/(1+q^n).
%F A096661 Dragonette's gamma(n) = A064053(n) = 4*a(n) if n>0.
%e A096661 G.f. = - x^2 + x^3 - x^4 + x^5 - x^6 + 2*x^7 - x^8 - x^10 + 2*x^11 - x^12 + ...
%p A096661 add( (-1)^n*q^((3*n^2+n)/2)/(1+q^n),n=1..10);
%t A096661 a[n_]:= SeriesCoefficient[Sum[(-1)^k*q^((3*k^2 + k)/2)/(1 + q^k), {k, 1, 2*nmax}], {q,0,n}]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, Feb 18 2018 *)
%o A096661 (PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=1, (sqrtint(24*n + 1) - 1) \ 6, (-1)^k * x^((3*k^2 + k)/2) / (1 + x^k), x * O(x^n)), n))}; /* _Michael Somos_, Mar 13 2006 */
%Y A096661 Cf. A064053, A097042.
%K A096661 sign
%O A096661 0,8
%A A096661 _N. J. A. Sloane_, Sep 15 2004