The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A107635 McKay-Thompson series of class 32a for the Monster group. 5
 1, 3, 3, 4, 9, 12, 15, 21, 30, 43, 54, 69, 94, 123, 153, 193, 252, 318, 391, 486, 609, 754, 918, 1119, 1376, 1680, 2019, 2432, 2946, 3540, 4220, 5034, 6015, 7157, 8463, 9999, 11835, 13956, 16374, 19206, 22542, 26376, 30750, 35829, 41745, 48526, 56250 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 = 0..1000 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994). Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions Index entries for McKay-Thompson series for Monster simple group FORMULA Expansion of q^(1/8) * (eta(q^2)^2 / (eta(q) * eta(q^4)))^3 in powers of q. Expansion of chi(x)^3 = phi(x) / psi(-x) in powers of x where phi(), psi(), chi() are Ramanujan theta functions. Given g.f. A(x), then B(q) = A(q^8) / q satisfies 0 = f(B(q), B(q^3)) where f(u, v) = (u^3 - v) * (v^3 - u) - 9*u*v. Euler transform of period 4 sequence [3, -3, 3, 0, ...]. G.f.: Product_{k>0} (1 + (-x)^k)^-3. a(n) = (-1)^n * A022598(n). a(n) ~ exp(Pi*sqrt(n/2)) / (2^(7/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015 G.f.: exp(3*Sum_{k>=1} x^k/(k*(1 - (-x)^k))). - Ilya Gutkovskiy, Jun 07 2018 EXAMPLE G.f. = 1 + 3*x + 3*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 15*x^6 + 21*x^7 + ... T32a = 1/q + 3*q^7 + 3*q^15 + 4*q^23 + 9*q^31 + 12*q^39 + 15*q^47 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2]^2 / (QPochhammer[ x] QPochhammer[ x^4]))^3, {x, 0, n}]; (* Michael Somos, Jun 29 2014 *) nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k+1))^3, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *) PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 / (eta(x + A) * eta(x^4 + A)))^3, n))}; CROSSREFS Cf. A022598. Sequence in context: A045794 A065678 A022598 * A132319 A130626 A175796 Adjacent sequences: A107632 A107633 A107634 * A107636 A107637 A107638 KEYWORD nonn AUTHOR Michael Somos, May 18 2005 STATUS approved

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

Last modified June 18 17:48 EDT 2024. Contains 373483 sequences. (Running on oeis4.)