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A260518 Expansion of psi(x)^2 * f(-x^3)^3 / f(-x) in powers of x where psi(), f() are Ramanujan theta functions. 3
1, 3, 5, 7, 8, 11, 13, 14, 17, 16, 21, 23, 25, 27, 21, 32, 33, 35, 37, 32, 42, 38, 45, 47, 40, 51, 56, 55, 50, 48, 61, 63, 64, 70, 56, 62, 73, 80, 77, 63, 81, 83, 74, 87, 72, 91, 98, 95, 104, 64, 101, 103, 105, 107, 88, 112, 98, 115, 114, 112, 121, 123, 125 (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..2500

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of psi(x) * psi(x^3) * f(x, x^2)^2 in powers of x where psi(), f() are Ramanujan theta functions.

Expansion of q^(-7/12) * eta(q^2)^4 * eta(q^3)^3 / eta(q)^3 in powers of q.

Euler transform of period 6 sequence [ 3, -1, 0, -1, 3, -4, ...].

G.f.: Product_{k>0} (1 - x^(2*k))^4 * (1 + x^k + x^(2*k))^3.

EXAMPLE

G.f. = 1 + 3*x + 5*x^2 + 7*x^3 + 8*x^4 + 11*x^5 + 13*x^6 + 14*x^7 + ...

G.f. = q^7 + 3*q^19 + 5*q^31 + 7*q^43 + 8*q^55 + 11*q^67 + 13*q^79 + ...

MATHEMATICA

a[ n_] := seriesCoefficient[ QPochhammer[ x^2]^4 QPochhammer[ x^3]^3 / QPochhammer[ 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)^4 * eta(x^3 + A)^3 / eta(x + A)^3, n))};

(PARI) q='q+O('q^99); Vec(eta(q^2)^4*eta(q^3)^3/eta(q)^3) \\ Altug Alkan, Aug 01 2018

CROSSREFS

Sequence in context: A184415 A050111 A090542 * A190333 A190061 A288624

Adjacent sequences:  A260515 A260516 A260517 * A260519 A260520 A260521

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 28 2015

STATUS

approved

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Last modified September 18 12:28 EDT 2020. Contains 337169 sequences. (Running on oeis4.)