OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
MAPLE
k:=4: with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:='a': b[1]:=etr(a): for t from 2 to k do b[t]:= etr(b[t-1]) od: a:= n-> `if`(n<2, n, b[k](n-1)): seq(a(n), n=0..30);
MATHEMATICA
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[ j]}]*b[n-j], {j, 1, n}]/n]; b]; A[n_, k_] := Module[{a, b, t}, b[1] = etr[a]; For[ t = 2, t <= k, t++, b[t] = etr[b[t-1]]]; a = Function[m, If[m == 1, 1, b[k][m-1]]]; a[n]]; Table[A[n, 4], {n, 0, 30} ] (* Jean-François Alcover, Mar 05 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
eigen,nonn
AUTHOR
Alois P. Heinz, Sep 07 2008
STATUS
approved