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 A112148 McKay-Thompson series of class 12B for the Monster group. 4
 1, 0, 6, -4, -3, 12, -8, -12, 30, -20, -30, 72, -46, -60, 156, -96, -117, 300, -188, -228, 552, -344, -420, 1008, -603, -732, 1770, -1048, -1245, 2976, -1776, -2088, 4908, -2900, -3420, 7992, -4658, -5460, 12756, -7408, -8583, 19944, -11564, -13344, 30756, -17744, -20448, 46944 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS G. C. Greubel, Table of n, a(n) for n = -1..1000 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of -5 + (1/q) * (phi(q)^3 * psi(-q)) / (phi(q^3) * psi(-q^3)^3) in powers of q where phi(), psi() are Ramanujan theta functions. a(n) = -(-1)^n * A007258(n). - Michael Somos, May 20 2015 a(n) = A187146(n) = A187147(n) = A187148(n) unless n=0. - Michael Somos, May 20 2015 EXAMPLE T12B = 1/q + 6*q - 4*q^2 - 3*q^3 + 12*q^4 - 8*q^5 - 12*q^6 + 30*q^7 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ -5 + 2 EllipticTheta[3, 0, q]^3 EllipticTheta[2, Pi/4, q^(1/2)] / (EllipticTheta[3, 0, q^3] EllipticTheta[2, Pi/4, q^(3/2)]^3), {q, 0, n}]; (* Michael Somos, May 20 2015 *) QP = QPochhammer; s = -5*q +QP[q^2]^14/(QP[q]^5*QP[q^3]*QP[q^4]^5* QP[q^6]^2*QP[q^12]) + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 16 2015, adapted from PARI *) PROG (PARI) {a(n) = my(A); if( n<-1, 0, n++; A =x * O(x^n); polcoeff( -5 * x + eta(x^2 + A)^14 / (eta(x + A)^5 * eta(x^3 + A) * eta(x^4 + A)^5 * eta(x^6 + A)^2 * eta(x^12 + A)), n))}; /* Michael Somos, May 20 2015 */ CROSSREFS Cf. A007258, A187146, A187147, A187148. Sequence in context: A268817 A020794 A268818 * A007258 A045488 A082530 Adjacent sequences:  A112145 A112146 A112147 * A112149 A112150 A112151 KEYWORD sign AUTHOR Michael Somos, Aug 28 2005 STATUS approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)