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A257402 Expansion of chi(x) * psi(-x^3) * psi(x^12) in powers of x where psi(), chi() are Ramanujan theta functions. 5
1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,34

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-11/6) * eta(q^2)^2 * eta(q^3) * eta(q^24)^2 / (eta(q) * eta(q^4) * eta(q^6)) in powers of q.

a(4*n) = A255318(n). a(4*n + 1) = A255319(n). a(4*n + 2) = a(4*n + 3) = 0.

EXAMPLE

G.f. = 1 + x + x^5 + x^8 + x^12 + x^13 + x^16 + x^17 + x^20 + x^21 + x^28 + ...

G.f. = q^11 + q^17 + q^41 + q^59 + q^83 + q^89 + q^107 + q^113 + q^131 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^2] EllipticTheta[ 2, 0, x^6] EllipticTheta[ 2, Pi/4, x^(3/2)] / (2^(3/2) x^(15/8)), {x, 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^3 + A) * eta(x^24 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)), n))};

CROSSREFS

Cf. A255318, A255319.

Sequence in context: A172099 A170957 A178725 * A230263 A139354 A124762

Adjacent sequences:  A257399 A257400 A257401 * A257403 A257404 A257405

KEYWORD

nonn

AUTHOR

Michael Somos, Apr 21 2015

STATUS

approved

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Last modified July 29 02:55 EDT 2021. Contains 346340 sequences. (Running on oeis4.)