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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
OFFSET
0,34
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
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
Sequence in context: A172099 A170957 A178725 * A359966 A230263 A139354
KEYWORD
nonn
AUTHOR
Michael Somos, Apr 21 2015
STATUS
approved