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A260545 Expansion of phi(-x^6)^2 / (chi(x) * phi(-x)^2) in powers of x where phi(), chi() are Ramanujan theta functions. 1
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 (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

M. 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 A160462

Adjacent sequences:  A260542 A260543 A260544 * A260546 A260547 A260548

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 28 2015

STATUS

approved

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Last modified July 14 15:26 EDT 2020. Contains 335729 sequences. (Running on oeis4.)