OFFSET
1,6
COMMENTS
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
KEYWORD
sign
AUTHOR
Michael Somos, Sep 02 2007
STATUS
approved