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A138521 Expansion of chi(-q)^5 / chi(-q^5) in powers of q where chi() is a Ramanujan theta function. 3
1, -5, 10, -15, 30, -55, 80, -120, 190, -285, 410, -585, 840, -1190, 1640, -2240, 3070, -4170, 5570, -7400, 9830, -12960, 16920, -21990, 28520, -36805, 47180, -60225, 76720, -97350, 122880, -154610, 194110, -242880, 302740, -376295, 466710, -577270, 711800 (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 (eta(q) / eta(q^2))^5 * eta(q^10) / eta(q^5) in powers of q.

Euler transform of period 10 sequence [ -5, 0, -5, 0, -4, 0, -5, 0, -5, 0, ...].

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v * ((u+1)^2 + v) - (v + 4 * u).

G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u - v)^4 - u * v * (u - 1) * (u + 4) * (v - 1) * (v + 4).

G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A095813.

G.f.: Product_{k>0} (1 + x^(5*k)) / (1 + x^k)^5.

a(n) = -5 * A138519(n) unless n=0. Convolution inverse of A132985.

a(n) = (-1)^n * A225701(n). - Michael Somos, Sep 15 2015

EXAMPLE

G.f. = 1 - 5*q + 10*q^2 - 15*q^3 + 30*q^4 - 55*q^5 + 80*q^6 - 120*q^7 + 190*q^8 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -q^5, q^5] / QPochhammer[ -q, q]^5, {q, 0, n}]; (* Michael Somos, Sep 15 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x + A) / eta(x^2 + A) )^5 * eta(x^10 + A) / eta(x^5 + A), n))};

CROSSREFS

Cf. A095813, A132985, A138519, A225701.

Sequence in context: A276514 A031471 A045206 * A225701 A022600 A067237

Adjacent sequences:  A138518 A138519 A138520 * A138522 A138523 A138524

KEYWORD

sign

AUTHOR

Michael Somos, Mar 23 2008

STATUS

approved

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Last modified April 8 05:55 EDT 2020. Contains 333312 sequences. (Running on oeis4.)