A002509 - OEIS

%I M3256 N1314 #25 Apr 09 2018 11:00:44

%S 1,-1,4,-5,15,-19,45,-52,118,-137,281,-316,625,-695,1331,-1444,2696,

%T -2907,5308,-5640,10122,-10650,18845,-19628,34241,-35378,61036,-62524,

%U 106783,-108593,183799,-185646,311625,-312800,521232,-520044,860728,-854151,1404871,-1386868,2267960,-2228161

%N Expansion of a modular function for Gamma_0(14).

%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 Alois P. Heinz, <a href="/A002509/b002509.txt">Table of n, a(n) for n = 4..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)*eta(14z)^11/(eta(2z)^5*eta(7z)^7)

%F Euler transform of period 14 sequence [ -1, 4, -1, 4, -1, 4, 6, 4, -1, 4, -1, 4, -1, 0, ...]. - _Michael Somos_, Nov 10 2005

%F a(2*n) - a(2*n-1) ~ exp(4*Pi*sqrt(n/7)) / (sqrt(2) * 7^(9/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 09 2018

%t QP = QPochhammer; A = x*O[x]^50; s = QP[x+A]*(QP[x^14+A]^11/QP[x^2+A]^5/ QP[x^7+A]^7); CoefficientList[s, x] (* _Jean-François Alcover_, Nov 29 2015, adapted from PARI *)

%o (PARI) {a(n)=local(A); if(n<4, 0, n-=4; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^14+A)^11/ eta(x^2+A)^5/eta(x^7+A)^7, n))} /* _Michael Somos_, Nov 10 2005 */

%K sign,easy

%O 4,3

%A _N. J. A. Sloane_

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