A260545 Expansion of phi(-x^6)^2 / (chi(x) * phi(-x)^2) in powers of x where phi(), chi() are Ramanujan theta functions.

1, 3, 9, 22, 50, 105, 208, 395, 722, 1280, 2210, 3728, 6163, 10006, 15986, 25169, 39104, 60022, 91106, 136870, 203664, 300368, 439321, 637568, 918530, 1314214, 1868153, 2639276, 3706994, 5177868, 7194304, 9945872, 13683986, 18740880, 25554084, 34697883

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 q^(-1/24) * eta(q^4) * eta(q^6)^4 / (eta(q)^3 * eta(q^12)^2) in powers of q.

Euler transform of period 12 sequence [ 3, 3, 3, 2, 3, -1, 3, 2, 3, 3, 3, 0, ...].

a(n) = A001935(3*n).

Example

G.f. = 1 + 3*x + 9*x^2 + 22*x^3 + 50*x^4 + 105*x^5 + 208*x^6 + 395*x^7 + ...
G.f. = q + 3*q^25 + 9*q^49 + 22*q^73 + 50*q^97 + 105*q^121 + 208*q^145 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^6]^2 QPochhammer[ x^4] / QPochhammer[ x]^3, {x, 0, n}];
a[ n_] := SeriesCoefficient[ QPochhammer[ x, -x] EllipticTheta[ 4, 0, x^6]^2 / EllipticTheta[ 4, 0, x]^2, {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^6 + A)^4 / (eta(x + A)^3 * eta(x^12 + A)^2), n))};

Crossrefs

Cf. A001935.

Sequence in context: A086817 A247188 A000715 * A034505 A143099 A365664

Adjacent sequences: A260542 A260543 A260544 * A260546 A260547 A260548

Keyword

nonn

Author

Michael Somos, Jul 28 2015

Status

approved