OFFSET
1,9
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..2500
FORMULA
Euler transform of period 36 sequence [-1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 Pi i t).
G.f.: Product_{k>0} (1 - x^k) * (1 - x^(36*k)) / ((1 - x^(4*k)) * (1 - x^9*k)).
a(6*n) = a(6*n + 4) = 0. a(6*n + 2) = -A092848(n).
Convolution inverse of A187020.
EXAMPLE
G.f. = q - q^2 - q^3 + q^5 - q^7 + q^8 + 2*q^9 - 3*q^11 + 2*q^13 - 3*q^15 + ...
MATHEMATICA
QP = QPochhammer; s = QP[q]*(QP[q^36]/(QP[q^4]*QP[q^9])) + O[q]^80; CoefficientList[s, q]
PROG
(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^36 + A) / (eta(x^4 + A) * eta(x^9 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Apr 07 2012
STATUS
approved