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A212907 Expansion of x^(-1/3) * psi(x^3) * c(x) / 3 in powers of x where psi() is a Ramanujan theta function and c() is a cubic AGM theta function. 4
1, 1, 2, 1, 3, 3, 2, 2, 2, 5, 3, 3, 4, 4, 3, 4, 3, 5, 3, 6, 6, 3, 4, 5, 5, 7, 5, 4, 4, 4, 8, 3, 6, 7, 9, 7, 5, 4, 3, 9, 7, 4, 7, 5, 10, 5, 8, 8, 4, 7, 9, 6, 8, 7, 8, 10, 5, 6, 5, 9, 10, 7, 8, 6, 7, 10, 7, 12, 6, 10, 7, 5, 12, 6, 12, 14, 6, 6, 5, 11, 6, 8, 10 (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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-17/24) * eta(q^3)^2 * eta(q^6)^2 / eta(q) in powers of q.

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

G.f.: Product_{k>0} (1 - x^(3*k))^2 * (1 - x^(6*k))^2 / (1 - x^k).

EXAMPLE

1 + x + 2*x^2 + x^3 + 3*x^4 + 3*x^5 + 2*x^6 + 2*x^7 + 2*x^8 + 5*x^9 + ...

q^17 + q^41 + 2*q^65 + q^89 + 3*q^113 + 3*q^137 + 2*q^161 + 2*q^185 + ...

MATHEMATICA

QP := QPochhammer; a[n_]:= SeriesCoefficient[(QP[q^3]*QP[q^6])^2/QP[q], {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)^2 * eta(x^6 + A)^2 / eta(x + A), n))}

CROSSREFS

Sequence in context: A035050 A198790 A306995 * A308584 A046819 A159945

Adjacent sequences:  A212904 A212905 A212906 * A212908 A212909 A212910

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 16 2012

STATUS

approved

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Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)