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A224825 Expansion of psi(x) * psi(x^3)^2 in powers of x where psi() is a Ramanujan theta function. 2
1, 1, 0, 3, 2, 0, 4, 1, 0, 5, 3, 0, 5, 4, 0, 5, 1, 0, 7, 5, 0, 7, 4, 0, 9, 0, 0, 7, 6, 0, 6, 6, 0, 11, 3, 0, 8, 5, 0, 10, 6, 0, 8, 2, 0, 9, 6, 0, 14, 8, 0, 10, 0, 0, 15, 7, 0, 7, 8, 0, 7, 4, 0, 14, 9, 0, 14, 6, 0, 16, 1, 0, 8, 11, 0, 13, 10, 0, 13, 0, 0, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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^(-7/8) * eta(q^2)^2 * eta(q^6)^4 / (eta(q) * eta(q^3)^2) in powers of q.

Euler transform of period 6 sequence [1, -1, 3, -1, 1, -3, ...].

G.f.: (Sum_{k>0} x^(k*(k-1)/2)) * (Sum_{k>0} x^(3 * k*(k-1)/2))^2.

a(3*n + 2) = 0. a(n) = A033768(3*n + 1). a(3*n + 1) = A224823(n).

EXAMPLE

G.f. = 1 + x + 3*x^3 + 2*x^4 + 4*x^6 + x^7 + 5*x^9 + 3*x^10 + 5*x^12 + 4*x^13 + ...

G.f. = q^7 + q^15 + 3*q^31 + 2*q^39 + 4*q^55 + q^63 + 5*q^79 + 3*q^87 + 5*q^103 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q^(1/2)] EllipticTheta[ 2, 0, q^(3/2)]^2 / (8 q^(7/8)), {q, 0, n}];

PROG

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

CROSSREFS

Cf. A033768, A224823.

Sequence in context: A005874 A275622 A129239 * A290794 A127571 A194662

Adjacent sequences:  A224822 A224823 A224824 * A224826 A224827 A224828

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 20 2013

STATUS

approved

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Last modified May 26 15:29 EDT 2019. Contains 323597 sequences. (Running on oeis4.)