A227900 Expansion of eta(q)^9 * eta(q^5)^3 in powers of q.

1, -9, 27, -12, -90, 132, 81, -180, -153, 185, 252, -324, 162, 396, -555, -1264, 936, 1377, -220, 1080, -1188, -2268, -3303, 2640, 4975, 792, 2430, -972, -6930, -11880, 6752, 5616, 6804, 4576, -1665, 1836, -18954, 1980, -2376, 3700, -198, 10692, 567, -3024

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

Cf. A227901.

Sequence in context: A359531 A365933 A109041 * A010817 A205973 A122985

Adjacent sequences: A227897 A227898 A227899 * A227901 A227902 A227903

Keyword

sign

Author

Michael Somos, Oct 15 2013

Status

approved