OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..2500
FORMULA
Euler transform of period 5 sequence [-9, -9, -9, -9, -12, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (5 t)) = 5^(9/2) (t/i)^6 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A227901.
G.f.: x * Product_{k>0} (1 - x^k)^9 * (1 - x^(5*k))^3.
EXAMPLE
G.f. = q - 9*q^2 + 27*q^3 - 12*q^4 - 90*q^5 + 132*q^6 + 81*q^7 - 180*q^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ q QPochhammer[ q]^9 QPochhammer[ q^5]^3, {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( (eta(x + A)^3 * eta(x^5 + A))^3, n))};
(Magma) A := Basis( CuspForms( Gamma1(5), 6), 45); A[1] - 9*A[2] + 27*A[3]; /* Michael Somos, Jan 08 2015 */
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 15 2013
STATUS
approved