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%I #16 Feb 09 2018 02:12:28
%S 3,4,12,0,15,12,12,0,24,12,24,0,15,16,36,0,24,24,12,0,48,12,36,0,27,
%T 24,36,0,24,36,36,0,48,12,48,0,24,28,48,0,51,36,24,0,72,24,24,0,24,36,
%U 84,0,48,36
%N a(n) = A005887(n) / 2.
%H G. C. Greubel, <a href="/A045826/b045826.txt">Table of n, a(n) for n = 0..1000</a>
%F Expansion of q^(-1) * (phi^3(q) - phi^3(-q)) / 4 in powers of q^2 where phi() is a Ramanujan theta function. - _Michael Somos_, Mar 12 2011
%F A005875(2*n + 1) = 2 * a(n). - _Michael Somos_, Mar 12 2011
%e 3 + 4*x + 12*x^2 + 15*x^4 + 12*x^5 + 12*x^6 + 24*x^8 + 12*x^9 + ...
%e 3*q + 4*q^3 + 12*q^5 + 15*q^9 + 12*q^11 + 12*q^13 + 24*q^17 + 12*q^19 + ...
%t A005887[n_]:= SeriesCoefficient[(EllipticTheta[3,0,q]^3 - EllipticTheta[3,0,-q]^3)/(2 q), {q, 0, n}]; Table[A005887[n]/2, {n,0, 50}][[1;; ;; 2]] (* _G. C. Greubel_, Feb 09 2018 *)
%o (PARI) {a(n) = if( n<0, 0, n = 2*n + 1; polcoeff( sum( k=1, sqrtint(n), 2 * x^k^2, 1 + x*O(x^n))^3 / 2, n))} /* _Michael Somos_, Mar 12 2011 */
%Y Cf. A005875, A005887.
%K nonn
%O 0,1
%A _N. J. A. Sloane_
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