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A260166 Expansion of phi(x^2) * f(-x^3)^3 / chi(-x)^2 in powers of x where phi(), chi(), f() are Ramanujan theta functions. 1
1, 2, 5, 7, 9, 11, 10, 15, 14, 19, 21, 21, 28, 24, 29, 26, 26, 35, 37, 39, 41, 34, 43, 47, 49, 56, 42, 55, 57, 50, 56, 50, 60, 74, 69, 76, 52, 70, 84, 79, 81, 66, 85, 74, 98, 91, 74, 88, 97, 99, 86, 84, 105, 107, 109, 122, 90, 98, 124, 119, 121, 105, 125, 127 (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^(-11/24) * eta(q^3)^3 * eta(q^4)^5 / (eta(q)^2 * eta(q^8)^2) in powers of q.

Euler transform of period 24 sequence [ 2, 2, -1, -3, 2, -1, 2, -1, -1, 2, 2, -6, 2, 2, -1, -1, 2, -1, 2, -3, -1, 2, 2, -4, ...].

3 * a(n) = A260158(4*n + 1).

EXAMPLE

G.f. = 1 + 2*x + 5*x^2 + 7*x^3 + 9*x^4 + 11*x^5 + 10*x^6 + 15*x^7 + 14*x^8 + ...

G.f. = q^11 + 2*q^35 + 5*q^59 + 7*q^83 + 9*q^107 + 11*q^131 + 10*q^155 + ...

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A260158.

Sequence in context: A174272 A062288 A077059 * A007300 A256699 A247421

Adjacent sequences:  A260163 A260164 A260165 * A260167 A260168 A260169

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 09 2015

STATUS

approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)