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A106508 Expansion of psi(x)^4 * chi(-x^2)^2 in powers of x where psi(), chi() are Ramanujan theta functions. 3
1, 4, 4, 0, 2, 0, -8, 0, -5, -16, 4, 0, -10, 0, -8, 0, 9, 8, 0, 0, 14, 0, 16, 0, -10, 32, 4, 0, 0, 0, 8, 0, 14, -20, -20, 0, 2, 0, 0, 0, -11, -16, -20, 0, -32, 0, 16, 0, 0, -40, 4, 0, 14, 0, -8, 0, -9, 32, -20, 0, 26, 0, 0, 0, 2, 36, 28, 0, 0, 0, 16, 0, 16, 0, 28, 0, -22, 0, 0, 0, 14, 56, -16, 0, 0, 0, -40, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

C. Adiga, N. Anitha and T. Kim, Transformations of Ramanujan's Summation Formula and its Applications, arXiv:math/0501528 [math.NT], 2005. See page 5.

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-1/3) * eta(q^2)^10 / (eta(q)^4 * eta(q^4)^2) in powers of q.

Euler transform of period 4 sequence [4, -6, 4, -4, ...].

a(n) = (-1)^n * A187149(n). a(4*n + 3) = a(8*n + 5) = 0.

G.f. Product_{k>0} (1 + x^k)^4 (1 - x^(2*k))^4 / (1 + x^(2*k))^2.

EXAMPLE

1 + 4*x + 4*x^2 + 2*x^4 - 8*x^6 - 5*x^8 - 16*x^9 + 4*x^10 - 10*x^12 + ...

q + 4*q^4 + 4*q^7 + 2*q^13 - 8*q^19 - 5*q^25 - 16*q^28 + 4*q^31 - 10*q^37 + ...

MATHEMATICA

a[n_]:= SeriesCoefficient[(x^(-1/2)/16)*EllipticTheta[2, 0, x^(1/2)]^4* QPochhammer[x^2, x^4]^2, {x, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 04 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^10 / (eta(x^4 + A)^2 * eta(x + A)^4), n))}

CROSSREFS

Cf. A187149.

Sequence in context: A131124 A131125 A187149 * A177036 A158100 A104287

Adjacent sequences:  A106505 A106506 A106507 * A106509 A106510 A106511

KEYWORD

sign

AUTHOR

Michael Somos, May 24 2005

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)