OFFSET
1,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
Michael Somos, A Remarkable eta-product Identity
FORMULA
Expansion of F(q) * F(q^2) in powers of q^3 where F(q) is the g.f. for A103263.
Euler transform of a period 60 sequence.
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 A143751.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u^2 + v^2) * (1 + u + v) * (u + v + u*v) - u*v * (1+ 2*u + 2*v + u*v)^2.
G.f.: x * Product_{k>0} P(30, x^k) * P(60, x^k) where P(n, x) is the n-th cyclotomic polynomial.
G.f.: -1 + Product_{k>0} (1 + x^k) * (1 + x^(15*k)) / ((1 + x^(6*k)) * (1 + x^(10*k))). - Seiichi Manyama, May 04 2017
a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 03 2018
EXAMPLE
G.f. = q + q^2 + 2*q^3 + 2*q^4 + 3*q^5 + 3*q^6 + 4*q^7 + 5*q^8 + 6*q^9 + 7*q^10 + ...
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 + A) * eta(x^12 + A) * eta(x^15 + A) * eta(x^20 + A)), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 31 2008
STATUS
approved