

A213627


Expansion of psi(x)^4 / psi(x^3) in powers of x where psi() is a Ramanujan theta function.


3



1, 4, 6, 7, 9, 6, 7, 15, 12, 12, 13, 6, 12, 18, 18, 13, 15, 18, 12, 24, 12, 13, 27, 12, 24, 15, 12, 24, 28, 30, 12, 27, 18, 12, 30, 18, 19, 27, 24, 24, 27, 24, 36, 30, 18, 19, 24, 24, 24, 45, 18, 12, 45, 30, 24, 28, 18, 36, 36, 36, 24, 15, 36, 36, 51, 18, 25
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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
M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions


FORMULA

Expansion of q^(1/8) * eta(q^2)^8 * eta(q^3) / (eta(q)^4 * eta(q^6)^2) in powers of q.
a(3*n + 2) = 6 * A212907(n).


EXAMPLE

G.f. = 1 + 4*x + 6*x^2 + 7*x^3 + 9*x^4 + 6*x^5 + 7*x^6 + 15*x^7 + 12*x^8 + ...
G.f. = q + 4*q^9 + 6*q^17 + 7*q^25 + 9*q^33 + 6*q^41 + 7*q^49 + 15*q^57 + 12*q^65 + ...


MATHEMATICA

a[ n_] := SeriesCoefficient[ 1/8 EllipticTheta[ 2, 0, q]^4 / EllipticTheta[ 2, 0, q^3], {q, 0, 2 n + 1/4}];


PROG

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


CROSSREFS

Cf. A212907.
Sequence in context: A078744 A024555 A269330 * A225871 A288383 A001690
Adjacent sequences: A213624 A213625 A213626 * A213628 A213629 A213630


KEYWORD

nonn


AUTHOR

Michael Somos, Jun 16 2012


STATUS

approved



