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A260295 Expansion of f(-x^2)^3 * f(-x^6)^3 / f(-x)^2 in powers of x where f() is a Ramanujan theta function. 3
1, 2, 2, 4, 5, 6, 7, 6, 9, 8, 11, 14, 10, 14, 15, 16, 14, 14, 19, 20, 21, 22, 21, 20, 28, 26, 24, 22, 29, 30, 26, 32, 26, 38, 35, 36, 37, 28, 39, 40, 41, 42, 34, 40, 43, 42, 47, 42, 49, 50, 56, 44, 42, 54, 55, 62, 57, 46, 50, 60, 56, 62, 50, 70, 60, 56, 74, 54 (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
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-11/12) * eta(q^2)^3 * eta(q^6)^3 / eta(q)^2 in powers of q.
Euler transform of period 6 sequence [2, -1, 2, -1, 2, -4, ...]. - Michael Somos, Aug 01 2018
EXAMPLE
G.f. = 1 + 2*x + 2*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 6*x^7 + ...
G.f. = q^11 + 2*q^23 + 2*q^35 + 4*q^47 + 5*q^59 + 6*q^71 + 7*q^83 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^3 QPochhammer[ x^6]^3 / QPochhammer[ x]^2, {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^6 + A)^3 / eta(x + A)^2, n))};
(PARI) q='q+O('q^99); Vec(eta(q^2)^3*eta(q^6)^3/eta(q)^2) \\ Altug Alkan, Jul 31 2018
CROSSREFS
Sequence in context: A059015 A325108 A329474 * A024683 A244017 A339022
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 07 2015
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)