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A213023 Expansion of psi(x)^2 * psi(-x^3) / chi(-x^2) in powers of x where psi(), chi() are Ramanujan theta functions. 4
1, 2, 2, 3, 2, 2, 4, 4, 5, 3, 4, 5, 4, 6, 4, 4, 5, 7, 5, 3, 6, 8, 8, 8, 6, 3, 7, 6, 10, 6, 5, 10, 4, 8, 7, 8, 10, 6, 9, 8, 5, 10, 10, 11, 6, 9, 11, 6, 12, 9, 8, 8, 10, 9, 6, 6, 15, 12, 9, 9, 6, 13, 10, 13, 10, 7, 14, 12, 12, 8, 7, 13, 10, 16, 9, 10, 10, 12 (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^(-17/24) * eta(q^2)^3 * eta(q^3) * eta(q^4) * eta(q^12) / (eta(q)^2 * eta(q^6)) in powers of q.

Euler transform of period 12 sequence [ 2, -1, 1, -2, 2, -1, 2, -2, 1, -1, 2, -3, ...].

a(n) = A180312(3*n + 1).

EXAMPLE

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

q^17 + 2*q^41 + 2*q^65 + 3*q^89 + 2*q^113 + 2*q^137 + 4*q^161 + 4*q^185 + ...

MATHEMATICA

QP := QPochhammer; a[n_]:=SeriesCoefficient[(QP[q^2]^3*QP[q^3]*QP[q^4] *QP[q^12])/(QP[q]^2*QP[q^6]), {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^2 + A)^3 * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A) / (eta(x + A)^2 * eta(x^6 + A)), n))}

CROSSREFS

Cf. A180312.

Sequence in context: A086454 A069360 A175509 * A068050 A210967 A275383

Adjacent sequences:  A213020 A213021 A213022 * A213024 A213025 A213026

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 03 2012

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)