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A187615 Expansion of f(-x^17, -x^19) + x^4 * f(-x, -x^35) in powers of x where f(,) is Ramanujan's general theta function. 1
1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Euler transform of period 36 sequence [ 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -2, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1, ...].

G.f.: Sum_{k in Z} (-1)^k * x^(18*k^2) * (x^(17*k + 4) + x^k).

a(n) = A133985(3*n). a(5*n + 1) = a(5*n + 3) = 0.

EXAMPLE

G.f. = 1 + x^4 - x^5 - x^17 - x^19 - x^39 + x^42 + x^70 + x^74 + x^110 + ...

G.f. = q + q^289 - q^361 - q^1225 - q^1369 - q^2809 + q^3025 + q^5041 + q^5329 + ...

MATHEMATICA

QP:= QPochhammer; a[n_]:= SeriesCoefficient[QP[q^36, q^36]*(QP[q^17, q^36]*QP[q^19, q^36] + q^4*QP[q, q^36]*QP[q^35, q^36]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Apr 04 2018 *)

PROG

(PARI) {a(n) = my(m); if( n<0, 0, if( issquare( 72*n + 1, &m), if( m%36 != 1, m=-m); if( m%36 == 1, m = (m-1) / 36, if( m%36 != 19, m=-m); if( m%36! = 19, return(0));  m = (m+17) / 36); (-1)^m))};

(PARI) {a(n) = my(A); if( n<0, 0, n*=3; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^5 / ( eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A) )^2, n))};

CROSSREFS

Cf. A133985.

Sequence in context: A095111 A166253 A159638 * A120528 A287663 A195376

Adjacent sequences:  A187612 A187613 A187614 * A187616 A187617 A187618

KEYWORD

sign

AUTHOR

Michael Somos, Mar 11 2011

STATUS

approved

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Last modified October 21 04:26 EDT 2019. Contains 328291 sequences. (Running on oeis4.)