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A213624 Expansion of psi(x)^2 * psi(x^4) in powers of x where psi() is a Ramanujan theta function. 9
1, 2, 1, 2, 3, 2, 4, 4, 2, 2, 5, 4, 2, 6, 3, 6, 7, 2, 5, 4, 5, 6, 6, 2, 5, 10, 3, 6, 10, 4, 6, 8, 3, 8, 7, 6, 7, 6, 4, 6, 11, 6, 9, 10, 3, 6, 14, 4, 8, 10, 8, 10, 5, 6, 4, 16, 7, 4, 10, 4, 13, 14, 7, 8, 8, 6, 10, 12, 7, 12, 15, 8, 8, 10, 4, 6, 17, 6, 10, 10 (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^(-3/4) * eta(q^2)^4 * eta(q^8)^2 / (eta(q)^2 * eta(q^4)) in powers of q.

Euler transform of period 8 sequence [ 2, -2, 2, -1, 2, -2, 2, -3, ...].

EXAMPLE

1 + 2*x + x^2 + 2*x^3 + 3*x^4 + 2*x^5 + 4*x^6 + 4*x^7 + 2*x^8 + 2*x^9 + ...

q^3 + 2*q^7 + q^11 + 2*q^15 + 3*q^19 + 2*q^23 + 4*q^27 + 4*q^31 + 2*q^35 + ...

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A029826 A192185 A246833 * A080845 A290370 A029166

Adjacent sequences:  A213621 A213622 A213623 * A213625 A213626 A213627

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 16 2012

STATUS

approved

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Last modified January 17 12:18 EST 2020. Contains 330958 sequences. (Running on oeis4.)