OFFSET
1,2
COMMENTS
(eta(q))^7/eta(7*q) in powers of (eta(7*q)/eta(q))^4.
This sequence is u_n in Theorem 6.5 in O'Brien's thesis.
REFERENCES
L. O'Brien, Modular forms and two new integer sequences at level 7, Massey University, 2016.
LINKS
L. O'Brien, Modular forms and two new integer sequences at level 7, Massey University, 2016.
FORMULA
(n+1)^4a_7(n+1)=-(26*n^4+52*n^3+58*n^2+32*n+7)a_7(n)-(267*n^4+268*n^2+18)a_7(n-1)-(1274*n^4-2548*n^3+2842*n^2-1568*n+343)a_7(n-2)-2401(n-1)^4a_7(n-3)
with a_7(0)=1, a_7(-1)=a_7(-2)=a_7(-3)=0.
asymptotic conjecture: a(n) ~ C n^(-4/3) 7^n cos( n( arctan( (3*sqrt 3)/13) +Pi -1.083913253)), where C = 6.502807770...
EXAMPLE
G.f.: 1 - 7*x + 42*x^2 - 231*x^3 + 1155*x^4 - 4998*x^5 + ...
CROSSREFS
KEYWORD
sign
AUTHOR
Lynette O'Brien, Dec 15 2016
STATUS
approved