A260164 Expansion of f(-x^8)^2 / f(-x) in powers of x where f() is a Ramanujan theta function.

1, 1, 2, 3, 5, 7, 11, 15, 20, 28, 38, 50, 67, 87, 113, 146, 186, 236, 299, 375, 468, 583, 721, 888, 1093, 1336, 1628, 1980, 2397, 2894, 3487, 4186, 5013, 5991, 7139, 8488, 10073, 11924, 14086, 16613, 19551, 22965, 26934, 31527, 36844, 42994, 50085, 58258

Offset

0,3

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-5/8) * eta(q^8)^2 / eta(q) in powers of q.

Euler transform of period 8 sequence [ 1, 1, 1, 1, 1, 1, 1, -1, ...].

2 * a(n) = A132965(2*n + 1).

Example

G.f. = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 20*x^8 + ...
G.f. = q^5 + q^13 + 2*q^21 + 3*q^29 + 5*q^37 + 7*q^45 + 11*q^53 + 15*q^61 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x^8]^2 / QPochhammer[ x], {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^8 + A)^2 / eta(x + A), n))};

Crossrefs

Cf. A010054, A132965.

Sequence in context: A090693 A260794 A277576 * A280938 A049756 A319472

Adjacent sequences: A260161 A260162 A260163 * A260165 A260166 A260167

Keyword

nonn

Author

Michael Somos, Nov 09 2015

Status

approved