login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A002509
Expansion of a modular function for Gamma_0(14).
(Formerly M3256 N1314)
2
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
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
KEYWORD
sign,easy
EXTENSIONS
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001
STATUS
approved