A095123 Expansion of ((eta(q)eta(q^15))/(eta(q^3)eta(q^5)))^3 in powers of q.

1, -3, 0, 8, -9, 3, 8, -27, 24, 19, -48, 24, 17, -54, 57, 46, -147, 51, 145, -222, 123, 160, -459, 315, 306, -678, 360, 326, -870, 633, 612, -1581, 723, 1286, -2301, 1242, 1522, -3864, 2451, 2455, -5478, 2934, 2924, -7044, 4599, 4622, -11271, 5514, 8133, -15591, 8508

Offset

1,2

Comments

G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=u^3+v^3+uv(-1+6(u+v)-uv).

Euler transform of period 15 sequence [ -3,-3,0,-3,0,0,-3,-3,0,0,-3,0,-3,-3,0,...].

References

B. C. Berndt, H. H. Chan, S.-S. Huang, Incomplete Elliptic Integrals in Ramanujan's Lost Notebook, in q-series from a Contemporary Perspective, M. E. H. Ismail and D. Stanton, eds., Amer. Math. Soc., 2000, pp. 79-126.

Links

Table of n, a(n) for n=1..51.

B. C. Berndt, H. H. Chan, S.-S. Huang, Incomplete Elliptic Integrals in Ramanujan's Lost Notebook.

Formula

G.f. x(Prod_{k>0} ((1-x^k)(1-x^(15k)))/(1-x^(3k))(1-x^(5k)))^3.

Prog

(PARI) a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff((eta(x+A)*eta(x^15+A)/eta(x^3+A)/eta(x^5+A))^3, n))

Crossrefs

Sequence in context: A199659 A201584 A281298 * A019691 A192919 A068607

Adjacent sequences: A095120 A095121 A095122 * A095124 A095125 A095126

Keyword

sign

Author

Michael Somos, May 28 2004

Status

approved