A143337 Expansion of K(k) * (6 * E(k) - (1 + 4*k'^2) * K(k)) / (Pi/2)^2 in powers of q where E(k), K(k) are complete elliptic integrals and q = exp(-Pi * K(k') / K(k)).
1, 24, -72, 96, -168, 144, -288, 192, -360, 312, -432, 288, -672, 336, -576, 576, -744, 432, -936, 480, -1008, 768, -864, 576, -1440, 744, -1008, 960, -1344, 720, -1728, 768, -1512, 1152, -1296, 1152, -2184, 912, -1440, 1344, -2160, 1008, -2304, 1056, -2016, 1872, -1728, 1152
Offset: 0
Keywords
Examples
G.f. = 1 + 24*q - 72*q^2 + 96*q^3 - 168*q^4 + 144*q^5 - 288*q^6 + 192*q^7 + ...
Programs
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Mathematica
a[ n_] := If[ n < 1, Boole[n == 0], -(-1)^n 24 DivisorSigma[ 1, n]]; (* Michael Somos, Apr 07 2015 *)
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PARI
{a(n) = if( n<1, n==0, -(-1)^n * 24 * sigma(n))};
Formula
G.f.: 1 - 24 * Sum_{k>0} k * (-x)^k / (1 - (-x)^k) = 1 - 24 * Sum_{k>0} (-x)^k / (1 - (-x)^k)^2.
a(n) = (-1)^n * A006352(n).
a(n) = 24 * A143348(n) unless n=0.
Expansion of -(P(q) - 6 * P(q^2) + 4 * P(q^4)) in powers of q where P() is a Ramanujan Lambert series. - Michael Somos, Apr 07 2015