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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 12:36 EST 2021. Contains 349563 sequences. (Running on oeis4.)