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A257920 Expansion of phi(x) * psi(x^3) in powers of x where phi(), psi() are Ramanujan theta functions. 6
1, 2, 0, 1, 4, 0, 0, 2, 0, 3, 2, 0, 2, 2, 0, 0, 2, 0, 3, 4, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 1, 2, 0, 0, 6, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 3, 4, 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 1, 4, 0, 2, 6, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 4, 2, 0, 3, 2, 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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-3/8) * eta(q^2)^5 * eta(q^6)^2 / (eta(q)^2 * eta(q^3) * eta(q^4)^2) in powers of q.

Euler transform of period 12 sequence [ 2, -3, 3, -1, 2, -4, 2, -1, 3, -3, 2, -2, ...].

a(n) = A129402(4*n + 1) = A134177(4*n + 1) = A000377(8*n + 3) = A192013(8*n + 3).

a(3*n + 2) = 0. a(3*n + 1) = 2 * A128591(n).

EXAMPLE

G.f. = 1 + 2*x + x^3 + 4*x^4 + 2*x^7 + 3*x^9 + 2*x^10 + 2*x^12 + 2*x^13 + ...

G.f. = q^3 + 2*q^11 + q^27 + 4*q^35 + 2*q^59 + 3*q^75 + 2*q^83 + 2*q^99 + ...

MATHEMATICA

a[ n_] := Seriescoefficient[ EllipticTheta[ 3, 0, x] EllipticTheta[ 2, 0, x^(3/2)] / (2 x^(3/8)), {x, 0, n}];

PROG

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

CROSSREFS

Cf. A000377, A128591, A129402, A134177, A192013.

Sequence in context: A174996 A286815 A256276 * A258210 A258228 A271584

Adjacent sequences:  A257917 A257918 A257919 * A257921 A257922 A257923

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 12 2015

STATUS

approved

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Last modified January 22 16:29 EST 2020. Contains 331152 sequences. (Running on oeis4.)