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A121361 Expansion of f(x^1, x^5) * psi(x^2) in powers of x where psi(), f() are Ramanujan theta functions. 19
1, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 1, 0, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 1, 3, 0, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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^(-7/12) * eta(q^2) * eta(q^3) * eta(q^4) * eta(q^12) /

(eta(q) * eta(q^6)) in powers of q.

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

2*a(n) = A093829(12*n + 7).

EXAMPLE

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

G.f. = q^7 + q^19 + q^31 + q^43 + q^67 + q^79 + 2*q^91 + q^103 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -x^1, x^6] QPochhammer[ -x^5, x^6] QPochhammer[ x^6] EllipticTheta[ 2, 0, x] / (2 x^(1/4)), {x, 0, n}]; (* Michael Somos, Sep 02 2014 *)

PROG

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

CROSSREFS

Cf. A093829.

Sequence in context: A212210 A127499 A198068 * A191907 A052343 A073484

Adjacent sequences:  A121358 A121359 A121360 * A121362 A121363 A121364

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 16 2006

STATUS

approved

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Last modified June 19 23:39 EDT 2019. Contains 324222 sequences. (Running on oeis4.)