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A182668 The n-th Fourier coefficient divided by 11 of L_1(tau) defined by A. O. L. Atkin in 1967. 2
1, 27, 338, 2835, 18566, 101955, 490253, 2121679, 8424520, 31120519, 108082568, 355805844, 1117485594, 3366122862, 9767102571, 27398599802, 74534162438, 197147428426, 508187725366, 1279132093597, 3149343999710, 7596355910693, 17974782074306, 41775768918777 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Atkin (1967) on page 22, equation (30), defines phi(tau) = eta(121*tau) / eta(tau), a modular function which satisfies phi(-1/(121*t)) = 11^(-1)/phi(t), where q = exp(2*Pi*i*t). On page 23, equation (33), he defines L_1(tau) = U phi(tau), where U is a Hecke operator so that the n-th Fourier coefficient of L_1 is the 11*n-th Fourier coefficient of phi. On page 26, he finds that L_1(tau) = 11*g_2(tau) + 2*11^2*g_3(tau) + 11^3*g_4(tau) + 11^4*g_5(tau), where g_2, g_3, g_4, g_5 are functions he previously defined. The n-th Fourier coefficient of L_1 is 11*a(n).

First differs from A076394 at a(12). - Omar E. Pol, Dec 24 2012

The sequence of coefficients of the q-expansion of phi(tau) coincides with the partition function A000041 for the first 120 terms. - N. J. A. Sloane, Dec 24 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14-32.

EXAMPLE

x + 27*x^2 + 338*x^3 + 2835*x^4 + 18566*x^5 + 101955*x^6 + 490253*x^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[ eta[q^121]/ eta[q]/11, {q, 0, 300}], q][[1 ;; -1 ;; 11]] (* G. C. Greubel, Aug 10 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<1, 0, n = 11*n - 5; A = x * O(x^n); polcoeff( eta(x^121 + A) / eta(x + A), n) / 11)}

CROSSREFS

Cf. A000041, A076394.

Sequence in context: A048709 A268973 A160223 * A076394 A133211 A178983

Adjacent sequences:  A182665 A182666 A182667 * A182669 A182670 A182671

KEYWORD

nonn,changed

AUTHOR

Michael Somos, Dec 24 2012

STATUS

approved

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Last modified August 5 16:03 EDT 2020. Contains 336213 sequences. (Running on oeis4.)