A258591 Expansion of (phi(-x^2) * phi(-x^4)^2 / phi(-x)^3)^2 in powers of x where phi() is a Ramanujan theta function.

1, 12, 80, 400, 1664, 6056, 19904, 60320, 171008, 458428, 1171552, 2872368, 6790656, 15544136, 34568576, 74901984, 158507008, 328277848, 666568592, 1329014992, 2605464320, 5028397952, 9563654976, 17942323424, 33232441344, 60814373780, 110029864416

Offset

0,2

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 (eta(q^2)^5 * eta(q^4)^3 / (eta(q)^6 * eta(q^8)^2))^2 in powers of q.

Euler transform of period 8 sequence [ 12, 2, 12, -4, 12, 2, 12, 0, ...].

a(n) = A260186(2*n).

Example

G.f. = 1 + 12*x + 80*x^2 + 400*x^3 + 1664*x^4 + 6056*x^5 + 19904*x^6 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^2]^2 EllipticTheta[ 4, 0, x^4]^4 / EllipticTheta[ 4, 0, x]^6, {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 * eta(x^4 + A)^3 / (eta(x + A)^6 * eta(x^8 + A)^2))^2, n))};

Crossrefs

Cf. A260186.

Sequence in context: A190216 A160559 A038734 * A058962 A203486 A187011

Adjacent sequences: A258588 A258589 A258590 * A258592 A258593 A258594

Keyword

nonn

Author

Michael Somos, Nov 06 2015

Status

approved