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A262050 Expansion of f(-x)^2 * f(-x^10) / phi(-x)^3 in powers of x where phi(), f() are Ramanujan theta functions. 1
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 (list; graph; refs; listen; history; text; internal format)
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

M. 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

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)