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A192323 Expansion of theta_3(q^3) * theta_3(q^5) in powers of q. 6
1, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 6, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

FORMULA

Expansion of (eta(q^6) * eta(q^10))^5 / (eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20))^2 in powers of q.

Euler transform of a period 60 sequence.

G.f.: (Sum_{k} x^(3 * k^2)) * (Sum_{k} x^(5 * k^2)).

a(3*n + 1) = a(4*n + 2) = a(5*n + 1) = a(5*n + 4) = 0. a(4*n) = A028956(n).

a(n) = A122855(n) - A140727(n). a(5*n) = A260671(n).

EXAMPLE

G.f. = 1 + 2*q^3 + 2*q^5 + 4*q^8 + 2*q^12 + 4*q^17 + 2*q^20 + 4*q^23 + 2*q^27 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^3] EllipticTheta[ 3, 0, q^5], {q, 0, n}];

PROG

(PARI) {a(n) = if( n<1, n==0, qfrep([3, 0; 0, 5], n)[n]*2)};

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^6 + A) * eta(x^10 + A))^5 / (eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A))^2, n))};

CROSSREFS

Cf. A028956, A122855, A140727, A260671.

Sequence in context: A298100 A303636 A073274 * A242848 A071957 A329186

Adjacent sequences:  A192320 A192321 A192322 * A192324 A192325 A192326

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 01 2011

STATUS

approved

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Last modified January 26 13:09 EST 2022. Contains 350598 sequences. (Running on oeis4.)