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A103640
Expansion of theta_4(q)^4 - theta_2(q)^4, where theta_2 and theta_4 are the Jacobi theta series.
2
1, -24, 24, -96, 24, -144, 96, -192, 24, -312, 144, -288, 96, -336, 192, -576, 24, -432, 312, -480, 144, -768, 288, -576, 96, -744, 336, -960, 192, -720, 576, -768, 24, -1152, 432, -1152, 312, -912, 480, -1344, 144, -1008, 768, -1056, 288, -1872
OFFSET
0,2
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
Eric Weisstein's World of Mathematics, Eisenstein Series
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
G.f.: theta_4(q)^4 - theta_2(q)^4. - Michael Somos, May 29 2005
a(n) = (-1)^n * A004011(n). - Michael Somos, Jun 01 2012
Expansion of phi(-q)^4 - 16*q*psi(q^2)^4 in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos, Aug 21 2014
EXAMPLE
G.f. = 1 - 24*q + 24*q^2 - 96*q^3 + 24*q^4 - 144*q^5 + 96*q^6 - 192*q^7 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q]^4 - EllipticTheta[ 2, 0, q]^4, {q, 0, n}]; (* Michael Somos, Jun 01 2012 *)
a[ n_] := With[{m = InverseEllipticNomeQ @x}, SeriesCoefficient[(1 - 2 m) (EllipticK[m] / (Pi/2))^2, {x, 0, n}]]; (* Michael Somos, Aug 21 2014 *)
a[ n_] := If[ n < 1, Boole[n == 0], -24 Sum[ (-1)^(n + d) n / d, { d, Divisors[ n]}]]; (* Michael Somos, Aug 21 2014 *)
a[ n_] := If[ n < 1, Boole[n == 0], -24 DivisorSum[ n, (-1)^(n + #) n / # &]]; (* Michael Somos, Aug 21 2014 *)
PROG
(PARI) {a(n) = if( n<1, n==0, (-1)^n * 24 * sumdiv(n, d, d%2*d))}; /* Michael Somos, May 29 2005 */
(Magma) A := Basis( ModularForms( Gamma0(4), 2), 46); A[1] - 24*A[2]; /* Michael Somos, Aug 21 2014 */
CROSSREFS
Cf. A004011.
Sequence in context: A183008 A022358 A122505 * A004011 A334570 A056465
KEYWORD
sign,look
AUTHOR
Ralf Stephan, Feb 18 2005
STATUS
approved