A262050 Expansion of f(-x)^2 * f(-x^10) / phi(-x)^3 in powers of x where phi(), f() are Ramanujan theta functions.

1, 4, 11, 28, 63, 132, 264, 504, 928, 1660, 2892, 4924, 8221, 13480, 21750, 34592, 54288, 84168, 129048, 195816, 294282, 438324, 647413, 948748, 1380107, 1993632, 2860984, 4080172, 5784560, 8154900, 11435142, 15953124, 22147824, 30604868, 42102636, 57672312

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..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-1/2) * eta(q^2)^3 * eta(q^10) / eta(q)^4 in powers of q.

Euler transform of period 10 sequence [ 4, 1, 4, 1, 4, 1, 4, 1, 4, 0, ...].

2 * a(n) = A138526(2*n + 1) = - A261968(2*n + 1).

Example

G.f. = 1 + 4*x + 11*x^2 + 28*x^3 + 63*x^4 + 132*x^5 + 264*x^6 + 504*x^7 + ...
G.f. = q + 4*q^3 + 11*q^5 + 28*q^7 + 63*q^9 + 132*q^11 + 264*q^13 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ x^10] / EllipticTheta[ 4, 0, x]^3, {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^10 + A) / eta(x + A)^4, n))};

Crossrefs

Cf. A138526, A261968.

Sequence in context: A289217 A329141 A090539 * A293628 A113478 A056601

Adjacent sequences: A262047 A262048 A262049 * A262051 A262052 A262053

Keyword

nonn

Author

Michael Somos, Sep 09 2015

Status

approved