A002509 Expansion of a modular function for Gamma_0(14). (Formerly M3256 N1314)

1, -1, 4, -5, 15, -19, 45, -52, 118, -137, 281, -316, 625, -695, 1331, -1444, 2696, -2907, 5308, -5640, 10122, -10650, 18845, -19628, 34241, -35378, 61036, -62524, 106783, -108593, 183799, -185646, 311625, -312800, 521232, -520044, 860728, -854151, 1404871, -1386868, 2267960, -2228161

Offset

4,3

References

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

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

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387.

Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

Formula

eta(z)*eta(14z)^11/(eta(2z)^5*eta(7z)^7)

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

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

Mathematica

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A330857 A066516 A047184 * A230983 A100234 A007390

Adjacent sequences: A002506 A002507 A002508 * A002510 A002511 A002512

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved