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A213607 Expansion of psi(x^4) * f(-x^3)^3 / f(-x) in powers of x where psi(), f() are Ramanujan theta functions. 5
1, 1, 2, 0, 3, 2, 4, 0, 3, 3, 4, 0, 4, 3, 6, 0, 7, 3, 4, 0, 6, 5, 4, 0, 7, 4, 8, 0, 7, 5, 8, 0, 5, 4, 10, 0, 8, 5, 6, 0, 7, 7, 8, 0, 11, 5, 10, 0, 9, 8, 8, 0, 5, 4, 12, 0, 14, 5, 8, 0, 10, 8, 8, 0, 11, 8, 10, 0, 10, 9, 14, 0, 10, 5, 10, 0, 15, 7, 6, 0, 10, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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^(-5/6) * eta(q^3)^3 * eta(q^8)^2 / (eta(q) * eta(q^4)) in powers of q.

Euler transform of period 24 sequence [ 1, 1, -2, 2, 1, -2, 1, 0, -2, 1, 1, -1, 1, 1, -2, 0, 1, -2, 1, 2, -2, 1, 1, -3, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 32^(1/2) (t/i)^(3/2) g(t) where q = exp(2 Pi i t) and g() is g.f. for A213618.

a(4*n + 3) = 0.  a(4*n + 2) = 2 * A213023(n).

EXAMPLE

1 + x + 2*x^2 + 3*x^4 + 2*x^5 + 4*x^6 + 3*x^8 + 3*x^9 + 4*x^10 + ...

q^5 + q^11 + 2*q^17 + 3*q^29 + 2*q^35 + 4*q^41 + 3*q^53 + 3*q^59 + 4*q^65 + ...

MATHEMATICA

QP := QPochhammer; a[n_]:= SeriesCoefficient[(QP[q^3]^3*QP[q^8]^2 )/( QP[q]*QP[q^4]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 07 2018 *)

PROG

(PARI) {a(n) = local(A); if ( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^3 * eta(x^8 + A)^2 / (eta(x + A) * eta(x^4 + A)), n))}

CROSSREFS

Cf. A213023, A213618.

Sequence in context: A077962 A338101 A338490 * A298932 A089196 A208435

Adjacent sequences:  A213604 A213605 A213606 * A213608 A213609 A213610

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 16 2012

STATUS

approved

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Last modified June 15 08:14 EDT 2021. Contains 345048 sequences. (Running on oeis4.)