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A261394 Expansion of phi(q)^4 / phi(q^3) in powers of q where phi() is a Ramanujan theta function. 2
1, 8, 24, 30, 8, 0, 36, 48, 24, 32, 48, 48, 30, 0, 48, 72, 8, 48, 96, 48, 0, 0, 96, 96, 36, 56, 48, 102, 48, 0, 120, 48, 24, 72, 48, 96, 32, 0, 96, 120, 48, 48, 144, 144, 48, 0, 96, 96, 30, 56, 120, 144, 0, 0, 108, 96, 48, 120, 144, 48, 72, 0, 144, 192, 8, 96 (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..2500

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Euler transform of period 12 sequence [ 8, -12, 6, -4, 8, -9, 8, -4, 6, -12, 8, -3, ...].

a(n) = A004013(12*n).

EXAMPLE

G.f. = 1 + 8*x + 24*x^2 + 30*x^3 + 8*x^4 + 36*x^6 + 48*x^7 + 24*x^8 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q]^4 / EllipticTheta[ 3, 0, q^3], {q, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^20 * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A)^8 * eta(x^4 + A)^8 * eta(x^6 + A)^5), n))};

CROSSREFS

Cf. A004013.

Sequence in context: A212861 A333961 A038524 * A162829 A303796 A175368

Adjacent sequences:  A261391 A261392 A261393 * A261395 A261396 A261397

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 17 2015

STATUS

approved

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)