A227901 Expansion of eta(q)^3 * eta(q^5)^9 in powers of q.

1, -3, 0, 5, 0, -9, 20, 0, -45, 0, 36, -18, 0, 135, 0, -104, -153, 0, -60, 0, 252, 367, 0, -450, 0, -270, 108, 0, 660, 0, -624, -756, 0, 405, 0, 2106, -220, 0, -900, 0, -1188, -63, 0, -765, 0, -1589, 3792, 0, 925, 0, 216, -878, 0, 1260, 0, 660, -6930, 0

Offset

2,2

Links

G. C. Greubel, Table of n, a(n) for n = 2..2500

Formula

Euler transform of period 5 sequence [-3, -3, -3, -3, -12, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (5 t)) = 5^(3/2) (t/i)^6 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A227900.

G.f.: x^2 * Product_{k>0} (1 - x^k)^3 * (1 - x^(5*k))^9.

Example

G.f. = q^2 - 3*q^3 + 5*q^5 - 9*q^7 + 20*q^8 - 45*q^10 + 36*q^12 - 18*q^13 + ...

Mathematica

a[ n_] := SeriesCoefficient[ q^2 QPochhammer[ q]^3 QPochhammer[ q^5]^9, {q, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<2, 0, n-=2; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^5 + A)^3)^3, n))};

Crossrefs

Cf. A227900.

Sequence in context: A239233 A051704 A049689 * A118657 A047760 A276908

Adjacent sequences: A227898 A227899 A227900 * A227902 A227903 A227904

Keyword

sign

Author

Michael Somos, Oct 15 2013

Status

approved