A260675 Expansion of psi(x^2) * phi(x^15) in powers of x where phi(), psi() are Ramanujan theta functions.

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

G. C. Greubel, Table of n, a(n) for n = 0..2500

Michael Somos, Introduction to Ramanujan theta functions

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

Adjacent sequences: A260672 A260673 A260674 * A260676 A260677 A260678

Keyword

nonn

Author

Michael Somos, Nov 14 2015

Status

approved