A245434 Expansion of (phi(x) / phi(x^2)) * (f(-x^3, -x^5) / f(-x^1, -x^7)) in powers of x where phi(), f() are Ramanujan theta functions.

1, 3, 1, -4, 0, 9, -1, -20, 1, 38, 1, -64, -2, 107, -2, -180, 3, 292, 4, -452, -4, 686, -5, -1044, 5, 1563, 6, -2276, -8, 3284, -9, -4724, 12, 6712, 13, -9408, -14, 13086, -17, -18112, 18, 24879, 21, -33864, -26, 45806, -28, -61696, 34, 82614, 39, -109892

Offset

0,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Euler transform of period 8 sequence [3, -5, 1, 2, 1, -5, 3, 0, ...].

a(n) = A245436(2*n - 1). a(2*n) = A245433(n).

Example

G.f. = 1 + 3*x + x^2 - 4*x^3 + 9*x^5 - x^6 - 20*x^7 + x^8 + 38*x^9 + ...
G.f. = 1/q + 3*q + q^3 - 4*q^5 + 9*q^9 - q^11 - 20*q^13 + q^15 + 38*q^17 + ...

Mathematica

f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; a:= CoefficientList[Series[(f[q, q]/f[q^2, q^2])*(f[-q^3, -q^5]/f[-q, -q^7]), {q, 0, 60}], q]]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Aug 06 2018 *)

Prog

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[0, -3, 5, -1, -2, -1, 5, -3][k%8 + 1]), n))};

Crossrefs

Cf. A245433, A245436.

Sequence in context: A021765 A267187 A274716 * A305100 A051512 A079668

Adjacent sequences: A245431 A245432 A245433 * A245435 A245436 A245437

Keyword

sign

Author

Michael Somos, Jul 21 2014

Status

approved