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A002508
Expansion of a modular function for Gamma_0(6).
(Formerly M1910 N0754)
2
1, -2, 9, -4, 28, 18, 118, 80, 504, 466, 1631, 2160, 5466, 7498, 17658, 25088, 51944, 78660, 149099, 226544, 412920, 627830, 1090006, 1671840, 2796805, 4263984, 6969690, 10555224, 16836620, 25396506, 39699240, 59409184, 91460952, 135795598, 205951071, 303740496, 454672142
OFFSET
3,2
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)^2*eta(6z)^22/(eta(2z)^10*eta(3z)^14).
Euler transform of period 6 sequence [ -2, 8, 12, 8, -2, 0, ...]. - Michael Somos, Nov 10 2005
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(27/4) * 3^(17/4) * n^(3/4)). - Vaclav Kotesovec, Apr 09 2018
MATHEMATICA
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 *)
PROG
(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 */
CROSSREFS
Reciprocal series to A002507. Cf. A002509.
Sequence in context: A302451 A220416 A054789 * A353242 A249596 A038215
KEYWORD
sign,easy
EXTENSIONS
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001
STATUS
approved