This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A035174 #23 May 25 2016 12:45:23 %S A035174 1,-24,-1472,84480,987136,-196706304,2699296768,338071388160, %T A035174 -13641873096704,-364965248630784,36697722069188608, %U A035174 -133296500464680960,-71957818786545926144,1999978883828768833536,99370119662955604738048 %N A035174 Ramanujan's tau function (or tau numbers (A000594)) for 2^n. %H A035174 Seiichi Manyama, <a href="/A035174/b035174.txt">Table of n, a(n) for n = 0..604</a> %H A035174 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-24,-2048). %F A035174 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. %t A035174 Table[ RamanujanTau[2^n], {n, 0, 14}] %o A035174 (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 %o A035174 (PARI) Vec(1/(1+24*x+2048*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Apr 28 2013 %o A035174 (Perl) use ntheory ":all"; say "$_ ",ramanujan_tau(1 << $_) for 0..63; # _Dana Jacobsen_, Sep 05 2015 %Y A035174 Cf. A000594, A064556. %K A035174 sign,easy %O A035174 0,2 %A A035174 _Robert G. Wilson v_, Jan 04 2003