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A298932 Expansion of f(-x^3)^3 * phi(-x^12) / (f(-x) * chi(-x^4)) in powers of x where phi(), chi(), f() are Ramanujan theta functions. 3
1, 1, 2, 0, 3, 2, 4, 0, 4, 4, 6, 0, 5, 3, 6, 0, 6, 4, 4, 0, 8, 4, 6, 0, 9, 6, 6, 0, 6, 6, 12, 0, 8, 4, 12, 0, 8, 7, 8, 0, 9, 6, 8, 0, 12, 8, 6, 0, 8, 6, 14, 0, 12, 6, 12, 0, 8, 8, 12, 0, 13, 6, 12, 0, 18, 10, 8, 0, 8, 12, 12, 0, 16, 7, 14, 0, 12, 8, 12, 0, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-1/2) * eta(q^3)^3 * eta(q^8) * eta(q^12)^2 / (eta(q) * eta(q^4) * eta(q^24)) in powers of q.

Euler transform of period 24 sequence [1, 1, -2, 2, 1, -2, 1, 1, -2, 1, 1, -3, 1, 1, -2, 1, 1, -2, 1, 2, -2, 1, 1, -3, ...].

a(4*n + 3) = 0. a(3*n + 2) = 2 * A213607(n). a(n) = A298931(3*n). a(2*n) = A298933(n).

EXAMPLE

G.f. = 1 + x + 2*x^2 + 3*x^4 + 2*x^5 + 4*x^6 + 4*x^8 + 4*x^9 + ...

G.f. = q + q^3 + 2*q^5 + 3*q^9 + 2*q^11 + 4*q^13 + 4*q^17 + 4*q^19 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^3 QPochhammer[ -x^4, x^4] EllipticTheta[ 4, 0, x^12] / QPochhammer[ x], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^3 * eta(x^8 + A) * eta(x^12 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^24 + A)), n))};

CROSSREFS

Cf. A213607, A298931, A298933.

Sequence in context: A077961 A077962 A213607 * A089196 A208435 A208457

Adjacent sequences:  A298929 A298930 A298931 * A298933 A298934 A298935

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 29 2018

STATUS

approved

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Last modified March 28 16:48 EDT 2020. Contains 333089 sequences. (Running on oeis4.)