The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002507 Expansion of a modular function for Gamma_0(6). (Formerly M1542 N0602) 12
 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 (list; graph; refs; listen; history; text; internal format)
 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: A181074 A078125 A034692 * A137094 A209866 A130379 Adjacent sequences:  A002504 A002505 A002506 * A002508 A002509 A002510 KEYWORD sign,easy AUTHOR EXTENSIONS More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 13 04:57 EDT 2021. Contains 342934 sequences. (Running on oeis4.)