cp's OEIS Frontend

A256624 a(n) = 2 * A153182(n) - A005875(n).

%I A256624 #19 Nov 29 2017 23:04:50
%S A256624 1,-2,-4,-8,-10,-8,-8,-16,-20,-10,-8,-24,-24,-8,-16,-32,-26,-16,-12,
%T A256624 -24,-40,-16,-8,-48,-40,-10,-24,-32,-32,-24,-16,-48,-52,-16,-16,-48,
%U A256624 -50,-8,-24,-64,-40,-32,-16,-24,-72,-24,-16,-80,-56,-18,-28,-48,-40,-24
%N A256624 a(n) = 2 * A153182(n) - A005875(n).
%H A256624 G. C. Greubel, <a href="/A256624/b256624.txt">Table of n, a(n) for n = 0..1000</a>
%H A256624 K. Bringmann and J. Lovejoy, <a href="http://arxiv.org/abs/0712.0631">Overpartitions and class numbers of binary quadratic forms</a>. See page 5, Corollary 1.6(iv), equation (1.12)
%F A256624 G.f.: (1 + 8 * Sum_{k > 0} (-1)^k * x^(k^2 + k) / (1 + (-x)^k)^2) / (1 + 2 * Sum_{k > 0} x^k^2).
%F A256624 a(n) = (-1)^n * A153181(n). - _Michael Somos_, Jul 12 2015
%e A256624 G.f. = 1 - 2*x - 4*x^2 - 8*x^3 - 10*x^4 - 8*x^5 - 8*x^6 - 16*x^7 - 20*x^8 + ...
%t A256624 a[ n_] := If[ n < 0, 0, SeriesCoefficient[ (1 + 8 Sum[ (-1)^ k x^(k^2 + k) / (1 + (-x)^k)^2, {k, (Sqrt[4 n + 1] - 1)/2}]) / EllipticTheta[ 3, 0, x], {x, 0, n}]]; Table[a[n], {n, 0, 50}]
%o A256624 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (1 + 8 * sum(k=1, (sqrtint(4*n + 1)-1)\2, (-1)^k * x^(k^2 + k) / (1 + (-x)^k)^2 , A)) / (1 + 2 * sum(k=1, sqrtint(n), x^k^2, A)), n))};
%Y A256624 Cf. A005875, A153181, A153182.
%K A256624 sign
%O A256624 0,2
%A A256624 _Michael Somos_, Jul 11 2015