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 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 (list; graph; refs; listen; history; text; internal format)
 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 EXTENSIONS More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001 STATUS approved

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Last modified September 27 08:13 EDT 2021. Contains 347689 sequences. (Running on oeis4.)