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A258093 Expansion of q^(-1) * psi(q) / psi(q^3)^3 in powers of q where psi() is a Ramanujan theta function. 4
1, 1, 0, -2, -3, 0, 4, 6, 0, -10, -12, 0, 20, 24, 0, -36, -45, 0, 64, 78, 0, -112, -132, 0, 189, 222, 0, -308, -363, 0, 492, 576, 0, -778, -900, 0, 1210, 1392, 0, -1844, -2121, 0, 2776, 3180, 0, -4144, -4716, 0, 6114, 6936, 0, -8914, -10098, 0, 12884, 14550 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

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 = -1..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of eta(q^2)^2 * eta(q^3)^3 / (eta(q) * eta(q^6)^6) in powers of q.

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

G.f.: x^-1 * Product_{k>0} ((1 - x^(2*k))^2 * (1 - x^(3*k))^3) / ((1 - x^k) * (1 - x^(6*k))^6).

a(3*n + 1) = 0. a(3*n) = A132979(n). a(3*n - 1) = A258092(n).

Convolution inverse is A093829. Convolution with A004016 is A258094.

EXAMPLE

G.f. = 1/q + 1 - 2*q^2 - 3*q^3 + 4*q^5 + 6*q^6 - 10*q^8 - 12*q^9 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (1/q) QPochhammer[ q^2]^2 QPochhammer[ q^3]^3 / (QPochhammer[ q] QPochhammer[ q^6]^6), {q, 0, n}]; (* Michael Somos, May 25 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 / (eta(x + A) * eta(x^6 + A)^6), n))};

CROSSREFS

Cf. A093289, A132979, A258092, A258094.

Sequence in context: A091246 A271439 A133637 * A286578 A010340 A049275

Adjacent sequences:  A258090 A258091 A258092 * A258094 A258095 A258096

KEYWORD

sign

AUTHOR

Michael Somos, May 19 2015

STATUS

approved

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Last modified June 1 18:43 EDT 2020. Contains 334762 sequences. (Running on oeis4.)