A002507 Expansion of a modular function for Gamma_0(6). (Formerly M1542 N0602)

1, 2, -5, -24, -23, 76, 249, 168, -599, -1670, -1026, 3272, 8529, 5232, -14062, -35976, -22337, 51516, 131617, 82568, -169376, -432636, -273332, 513584, 1309800, 830372, -1456569, -3709672, -2354215, 3904696, 9931407, 6301120, -9983208, -25339626, -16057040, 24504584, 62033318

Offset

-3,2

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

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 = -3..10000

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

Expansion of q^-3 * psi(q)^6 * phi(-q)^2 in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos, Apr 24 2014

Expansion of eta(q^2)^10 * eta(q^3)^14 / (eta(q)^2 * eta(q^6)^22) in powers of q.

Euler transform of period 6 sequence [2, -8, -12, -8, 2, 0, ...]. - Michael Somos, Nov 10 2005

Convolution product of A128632, A128633, and A105559 (all three of them are modular functions and McKay-Thompson series of class 6E for the monster group). - Michael Somos, May 23 2014

Example

G.f. = q^-3 + 2*q^-2 - 5*q^-1 - 24 - 23*q + 76*q^2 + 249*q^3 + 168*q^4 + ...

Mathematica

QP = QPochhammer; s = QP[q^2]^10*(QP[q^3]^14/(QP[q]^2*QP[q^6]^22)) + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 14 2015, adapted from PARI *)

Prog

(PARI) {a(n) = local(A); if( n<-3, 0, n+=3; A = x * O(x^n); polcoeff( eta(x^2 + A)^10 * eta(x^3 + A)^14 / (eta(x + A)^2 * eta(x^6 + A)^22), n))}; /* Michael Somos, Nov 10 2005 */

Crossrefs

Cf. A002508, A105559, A128632, A128633.

Sequence in context: A078125 A034692 A347525 * A137094 A209866 A130379

Adjacent sequences: A002504 A002505 A002506 * A002508 A002509 A002510

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