login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Ramanujan's tau function (or tau numbers (A000594)) for 10^n.
3

%I #11 Jul 01 2023 16:13:08

%S 1,-115920,37534859200,-30328412970240000,-482606811957501440000,

%T -2983637890141033828147200000

%N Ramanujan's tau function (or tau numbers (A000594)) for 10^n.

%H Seiichi Manyama, <a href="/A064556/b064556.txt">Table of n, a(n) for n = 0..181</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-115920, 124097412800, -11592000000000000, -10000000000000000000000).

%t Table[ RamanujanTau[10^n], {n, 0, 5}]

%o (Perl) use bigint; use ntheory ":all"; say "$_ ",ramanujan_tau(10 ** $_) for 0..19; # _Dana Jacobsen_, Sep 05 2015

%o (PARI) taup(p, e)={

%o if(e==1,

%o (65*sigma(p, 11)+691*sigma(p, 5)-691*252*sum(k=1, p-1, sigma(k, 5)*sigma(p-k, 5)))/756

%o ,

%o my(t=taup(p, 1));

%o sum(j=0, e\2,

%o (-1)^j*binomial(e-j, e-2*j)*p^(11*j)*t^(e-2*j)

%o )

%o )

%o };

%o a(n)=taup(5,n)*taup(2,n) \\ _Charles R Greathouse IV_, Sep 06 2015

%Y Cf. A000594, A035174.

%K sign

%O 0,2

%A _Robert G. Wilson v_, Jan 04 2003