A002508 - OEIS

%I M1910 N0754 #26 Apr 09 2018 08:24:51

%S 1,-2,9,-4,28,18,118,80,504,466,1631,2160,5466,7498,17658,25088,51944,

%T 78660,149099,226544,412920,627830,1090006,1671840,2796805,4263984,

%U 6969690,10555224,16836620,25396506,39699240,59409184,91460952,135795598,205951071,303740496,454672142

%N Expansion of a modular function for Gamma_0(6).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vaclav Kotesovec, <a href="/A002508/b002508.txt">Table of n, a(n) for n = 3..1000</a>

%H Morris Newman, <a href="http://plms.oxfordjournals.org/content/s3-9/3/373.extract">Construction and application of a class of modular functions (II)</a>. Proc. London Math. Soc. (3) 9 1959 373-387.

%H Morris Newman, <a href="/A002507/a002507.pdf">Construction and application of a class of modular functions, II</a>, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

%F eta(z)^2*eta(6z)^22/(eta(2z)^10*eta(3z)^14).

%F Euler transform of period 6 sequence [ -2, 8, 12, 8, -2, 0, ...]. - _Michael Somos_, Nov 10 2005

%F a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(27/4) * 3^(17/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 09 2018

%t QP = QPochhammer; s = QP[q]^2*QP[q^6]^22/(QP[q^2]^10*QP[q^3]^14) + O[q]^40; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 30 2015, adapted from PARI *)

%o (PARI) {a(n)=local(A); if(n<3, 0, n-=3; A=x*O(x^n); polcoeff( eta(x+A)^2*eta(x^6+A)^22/ eta(x^2+A)^10/eta(x^3+A)^14, n))} /* _Michael Somos_, Nov 10 2005 */

%Y Reciprocal series to A002507. Cf. A002509.

%K sign,easy

%O 3,2

%A _N. J. A. Sloane_

%E More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001