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A213622 Expansion of phi(x) * psi(x) * phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions. 6
1, 3, 4, 7, 8, 4, 9, 8, 4, 16, 9, 8, 20, 8, 8, 11, 8, 12, 20, 20, 8, 15, 16, 12, 20, 16, 8, 24, 21, 8, 20, 8, 16, 28, 24, 8, 17, 32, 12, 36, 16, 8, 24, 16, 24, 19, 20, 20, 32, 16, 12, 28, 16, 20, 44, 27, 12, 36, 24, 16, 28, 24, 16, 28, 32, 12, 25, 32, 12, 48 (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^(-1/8) * eta(q^2)^5 * eta(q^4)^3 / (eta(q)^3 * eta(q^8)^2), in powers of q.

Euler transform of period 8 sequence [ 3, -2, 3, -5, 3, -2, 3, -3, ...].

EXAMPLE

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

q + 3*q^9 + 4*q^17 + 7*q^25 + 8*q^33 + 4*q^41 + 9*q^49 + 8*q^57 + 4*q^65 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 1/2 EllipticTheta[ 2, 0, q] EllipticTheta[ 3, 0, q^2] EllipticTheta[ 3, 0, q^4], {q, 0, 2 n + 1/4}]; Table[a[n], {n, 0, 80}]

PROG

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

CROSSREFS

Sequence in context: A054058 A056007 A316973 * A246847 A193406 A104426

Adjacent sequences:  A213619 A213620 A213621 * A213623 A213624 A213625

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 16 2012

STATUS

approved

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Last modified February 21 23:41 EST 2020. Contains 332113 sequences. (Running on oeis4.)