OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..604
Index entries for linear recurrences with constant coefficients, signature (-24,-2048).
FORMULA
G.f.: 1/(1 + 24x + 2048x^2). Proof by Robin Chapman: Follows from the formula tau(p^{n+2}) = tau(p)tau(p^{n+1}) - p^11 tau(p^n) for prime p, which comes from the theory of Hecke operators on modular forms. The p = 2 case gives a recurrence for tau(2^n) leading immediately to the g.f.
MATHEMATICA
Table[ RamanujanTau[2^n], {n, 0, 14}]
PROG
(PARI) a(n)=sum(j=0, n\2, (-1)^j*binomial(n-j, n-2*j)*2^(11*j)*(-24)^(n-2*j)) \\ Charles R Greathouse IV, Apr 28 2013
(PARI) Vec(1/(1+24*x+2048*x^2)+O(x^99)) \\ Charles R Greathouse IV, Apr 28 2013
(Perl) use ntheory ":all"; say "$_ ", ramanujan_tau(1 << $_) for 0..63; # Dana Jacobsen, Sep 05 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Robert G. Wilson v, Jan 04 2003
STATUS
approved