OFFSET
0,2
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
a(0) = 1, a(n) = -(5/n)*Sum_{k=1..n} A116073(k)*a(n-k) for n > 0.
Expansion of q^(5/6) * eta(q)^5 / eta(q^5)^5 in powers of q. - Michael Somos, Apr 29 2017
Expansion of f(-x)^5 / f(-x^5)^5 in powers of x where f() is a Ramanujan theta function. - Michael Somos, Apr 29 2017
Euler transform of period 5 sequence [-5, -5, -5, -5, 0, ...]. - Michael Somos, Apr 29 2017
EXAMPLE
G.f. = 1 - 5*x + 5*x^2 + 10*x^3 - 15*x^4 - x^5 - 30*x^6 + 50*x^7 + 65*x^8 - 95*x^9 + ...
G.f. = q^-5 - 5*q + 5*q^7 + 10*q^13 - 15*q^19 - q^25 - 30*q^31 + 50*q^37 + 65*q^43 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x]^5 / QPochhammer[ x^5]^5, {x, 0, n}]; (* Michael Somos, Apr 29 2017 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) / eta(x^5 + A))^5, n))}; /* Michael Somos, Apr 29 2017 */
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 29 2017
STATUS
approved