|
%I #19 Mar 01 2021 06:08:03
%S 1,1,0,-1,-1,0,1,0,-1,0,2,1,-3,-3,4,7,-4,-14,3,28,4,-53,-30,91,95,
%T -142,-240,191,556,-165,-1192,-140,2358,1215,-4322,-4194,7211,11492,
%U -10300,-27839,10194,61770,3506,-127099,-58080,242071,218346,-419278
%N Shifts left under inverse Euler transform.
%H Alois P. Heinz, <a href="/A038071/b038071.txt">Table of n, a(n) for n = 1..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p with(numtheory): ietr:= proc(p) local a, c; c:= proc(n) option remember; local j; n*p(n)-add(c(j)*p(n-j), j=1..n-1) end; a:=proc(n) option remember; local d; `if`(n=0, 1, add(mobius(n/d)*c(d), d=divisors(n))/n) end end: aa:= ietr('a'): a:= n-> `if`(n<=1,1, aa(n-1)): seq(a(n), n=1..48); # _Alois P. Heinz_, Sep 08 2008
%t ietr[p_] := Module[{a, c},
%t c[n_] := c[n] = n*p[n] - Sum[c[j]*p[n-j], {j, 1, n-1}];
%t a[n_] := a[n] = If[n == 0, 1, Sum[MoebiusMu[n/d]*c[d],
%t {d,Divisors[n]}]/n]; a];
%t aa = ietr[a];
%t a[n_] := If[n <= 1, 1, aa[n-1]];
%t Array[a, 48] (* _Jean-François Alcover_, Mar 01 2021, after _Alois P. Heinz_ *)
%K sign,eigen
%O 1,11
%A _Christian G. Bower_, Jan 04 1999
|
