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A260675
Expansion of psi(x^2) * phi(x^15) in powers of x where phi(), psi() are Ramanujan theta functions.
2
1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0
OFFSET
0,16
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^(-1/4) * eta(q^4)^2 * eta(q^30)^5 / (eta(q^2) * eta(q^15)^2 * eta(q^60)^2) in powers of q.
Euler transform of a period 60 sequence.
2 * a(n) = A260671(4*n + 1).
EXAMPLE
G.f. = 1 + x^2 + x^6 + x^12 + 2*x^15 + 2*x^17 + x^20 + 2*x^21 + 2*x^27 + ...
G.f. = q + q^9 + q^25 + q^49 + 2*q^61 + 2*q^69 + q^81 + 2*q^85 + 2*q^109 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/2) x^(-1/4) EllipticTheta[ 2, 0, x] EllipticTheta[ 3, 0, x^15], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^2 * eta(x^30 + A)^5 / (eta(x^2 + A) * eta(x^15 + A)^2 * eta(x^60 + A)^2), n))};
CROSSREFS
Cf. A260671.
Sequence in context: A254886 A030219 A287345 * A035147 A101673 A091395
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 14 2015
STATUS
approved