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A329958 Expansion of q^(-13/24) * eta(q^2)^3 * eta(q^3) * eta(q^6) / eta(q)^2 in powers of q. 1
1, 2, 2, 3, 3, 4, 4, 3, 5, 3, 6, 7, 4, 5, 4, 8, 6, 5, 7, 6, 7, 8, 7, 5, 8, 10, 9, 4, 7, 7, 9, 11, 8, 10, 5, 10, 12, 7, 10, 8, 10, 12, 4, 10, 8, 13, 15, 10, 9, 5, 15, 9, 12, 11, 10, 12, 10, 11, 11, 12, 15, 12, 6, 14, 8, 11, 17, 13, 12, 9, 16, 17, 8, 15, 10, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..75.

FORMULA

Euler transform of period 6 sequence [2, -1, 1, -1, 2, -3, ...].

G.f.: Product_{k>=1} (1 + x^k)^2 * (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(6*k)).

Convolution of A033762 and A080995. Convolution of A010054 and A121444.

G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = (3/2)^(1/2) (t/i)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A329955.

EXAMPLE

G.f. = 1 + 2*x + 2*x^2 + 3*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 3*x^7 + 5*x^8 + ...

G.f. = q^13 + 2*q^37 + 2*q^61 + 3*q^85 + 3*q^109 + 4*q^133 + 4*q^157 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^3 QPochhammer[ x^3] QPochhammer[ x^6] / QPochhammer[ x]^2, {x, 0, n}];

PROG

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

CROSSREFS

Cf. A010054, A033762, A080995, A121444, A329955.

Sequence in context: A234475 A339082 A329907 * A309969 A036041 A252759

Adjacent sequences:  A329955 A329956 A329957 * A329959 A329960 A329961

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 26 2019

STATUS

approved

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Last modified May 7 08:54 EDT 2021. Contains 343636 sequences. (Running on oeis4.)