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A132967 Expansion of q * chi(-q^3) * chi(-q^5) / ( chi(-q^2) * chi(-q^30) ) in powers of q where chi() is a Ramanujan theta function. 3
1, 0, 1, -1, 1, -2, 2, -2, 3, -4, 4, -5, 6, -6, 9, -11, 10, -14, 16, -17, 22, -24, 26, -32, 37, -40, 47, -54, 58, -70, 80, -84, 100, -112, 122, -143, 158, -172, 198, -222, 242, -274, 306, -332, 379, -422, 454, -515, 569, -620, 698, -766, 834, -932, 1028, -1118 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Michael Somos, Introduction to Ramanujan theta functions

Michael Somos, A Remarkable eta-product Identity

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of eta(q^3) * eta(q^4) * eta(q^5) * eta(q^60) / (eta(q^2) * eta(q^6) * eta(q^10) * eta(q^30)) in powers of q.

Euler transform of period 60 sequence [0, 1, -1, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, 1, -1, 0, 0, 2, 0, 0, -1, 1, -1, 0, 0, 1, -1, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, -1, 1, 0, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = g(t) where q = exp(2 Pi i t) and g() is the g.f. for A132968.

G.f.: x * Product_{k>0} (1 + x^(2*k)) * (1 + x^(30*k)) / ( (1 + x^(3*k)) * (1 + x^(5*k)) ).

a(n) = - A132968(n) unless n=0.

EXAMPLE

G.f. = q + q^3 - q^4 + q^5 - 2*q^6 + 2*q^7 - 2*q^8 + 3*q^9 - 4*q^10 + 4*q^11 - ...

PROG

(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x*O(x^n); polcoeff( eta(x^3 + A) * eta(x^4 + A) * eta(x^5 + A) * eta(x^60 + A) / (eta(x^2 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^30 + A)), n))};

CROSSREFS

Cf. A132968.

Sequence in context: A067357 A051059 A132968 * A029075 A029052 A131795

Adjacent sequences:  A132964 A132965 A132966 * A132968 A132969 A132970

KEYWORD

sign

AUTHOR

Michael Somos, Sep 02 2007

STATUS

approved

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Last modified August 2 05:02 EDT 2021. Contains 346409 sequences. (Running on oeis4.)