A124243 Expansion of q*psi(q^9)/psi(q) in powers of q.

1, -1, 1, -2, 3, -4, 5, -7, 10, -12, 15, -20, 26, -32, 39, -50, 63, -76, 92, -114, 140, -168, 201, -244, 295, -350, 415, -496, 591, -696, 818, -967, 1140, -1332, 1554, -1820, 2126, -2468, 2861, -3324, 3855, -4448, 5126, -5916, 6816, -7824, 8970, -10292, 11793, -13471, 15372, -17548

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Expansion of eta(q)/eta(q^9)*(eta(q^18)/eta(q^2))^2 in powers of q.

Euler transform of period 18 sequence [ -1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 0, ...].

G.f.: A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v +v*(2*u -3*u^2 +v).

G.f.: x*Product_{k>0} (1-x^k)*(1-x^(18k))^2/((1-x^(2k))^2*(1-x^(9k))).

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n)/3) / (2*3^(3/2)*n^(3/4)). - Vaclav Kotesovec, Nov 16 2017

Mathematica

eta[x_] := x^(1/24)*QPochhammer[x]; A124243[n_] := SeriesCoefficient[ (eta[q]/eta[q^9])*(eta[q^18]/eta[q^2])^2, {q, 0, n}]; Table[A124243[n], {n, 0, 50}] (* G. C. Greubel, Aug 26 2017 *)

Prog

(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^18+A)^2/eta(x^2+A)^2/eta(x^9+A), n))}

Crossrefs

Sequence in context: A022957 A036028 A036033 * A132975 A213267 A145977

Adjacent sequences: A124240 A124241 A124242 * A124244 A124245 A124246

Keyword

sign

Author

Michael Somos, Oct 28 2006

Status

approved