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A107034 Expansion of f(-x) * f(-x^4) in powers of x where f() is a Ramanujan theta function. 2
1, -1, -1, 0, -1, 2, 1, 1, -1, 0, 1, -1, -1, -1, 0, -2, 1, 0, 0, 1, 2, -1, 0, 1, 0, 1, 0, 1, 1, -1, -3, 0, -1, 1, -1, -1, 0, 0, 0, 1, -2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, -1, 1, -3, 0, 1, 0, -1, -1, 0, 1, 0, 0, -2, 0, -1, -1, 0, -2, 1, 1, 0, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

REFERENCES

H. Kahl, G. Koehler, Components of Hecke theta series, J. Math. Anal. Appl. 232 (1999), no. 2, 312-331, see page 320. MR1683136 (2000e:11051)

LINKS

Table of n, a(n) for n=0..78.

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of f(x)^2 / chi(x)^3 = f(x)^5 / phi(x)^3 = f(-x^2)^2 / chi(x) = f(-x^2) * psi(-x) = f(-x^2)^3 / f(x) = phi(x)^2 / chi(x)^5 = psi(-x)^2 * chi(x) in powers of x where phi(), psi(), chi(), f() are Ramanujan theta functions. - Michael Somos, Jan 29 2015

Expansion of q^(-5/24) * eta(q) * eta(q^4) in powers of q.

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

G.f. Product_{k>0} (1 - x^k) * (1 - x^(4*k)).

EXAMPLE

G.f. = 1 - x - x^2 - x^4 + 2*x^5 + x^6 + x^7 - x^8 + x^10 - x^11 - x^12 - ...

G.f. = q^5 - q^29 - q^53 - q^101 + 2*q^125 + q^149 + q^173 - q^197 + q^245 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x] QPochhammer[ x^4], {x, 0, n}]; (* Michael Somos, Jan 29 2015 *)

PROG

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

CROSSREFS

Sequence in context: A117195 A156606 A194087 * A117410 A240009 A281490

Adjacent sequences:  A107031 A107032 A107033 * A107035 A107036 A107037

KEYWORD

sign

AUTHOR

Michael Somos, May 09 2005

STATUS

approved

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Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)