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A089805
Expansion of Jacobi theta function (theta_4(q^6) - theta_4(q^(2/3)))/2/q^(2/3).
1
1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,1
LINKS
G. E. Andrews, An introduction to Ramanujan's "lost" notebook, Amer. Math. Monthly 86 (1979), no. 2, 89-108.
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
a(2*n) = A089801(n). a(2*n + 1) = 0. - Michael Somos, Jun 30 2015
From Peter Bala, Feb 15 2021: (Start)
G.f.: Sum_{n >= 0} (-1)^n*q^(6*n^2+4*n)*(1 - q^(4*n+2)) = 1 - x^2 - x^10 + x^16 + x^32 - x^42 - x^66 + + - - ....
Note the identity of Ramanujan: Sum_{n >= 0} q^n/Product_{k = 0..n} 1 + q^(2*k+1) = Sum_{n >= 0} (-1)^n*q^(6*n^2+4*n)*(1 + q^(4*n+2)) = 1 + x^2 - x^10 - x^16 + x^32 + x^42 - - + + .... See Andrews, equation 1.2. (End)
MATHEMATICA
A089805[n_] := SeriesCoefficient[(EllipticTheta[4, 0, q^6] - EllipticTheta[4, 0, q^(2/3)])/(2*q^(2/3)), {q, 0, n}]; Table[A089805[n], {n, 0, 50}] (* G. C. Greubel, Nov 20 2017 *)
CROSSREFS
Cf. A089801.
Sequence in context: A016391 A016378 A323513 * A080116 A016359 A014029
KEYWORD
sign,easy
AUTHOR
Eric W. Weisstein, Nov 12 2003
STATUS
approved