|
%I #13 Jun 24 2018 18:56:57
%S 0,1,1,5,19,89,410,2052,10440,54874,293549,1597621,8807766,49107289,
%T 276358791,1567866228,8957204966,51486464912,297548288251,
%U 1727856600935,10076859047404,58996263573440,346614270372761,2042929868812385,12076076910981403
%N Shifts left when Euler transform applied 4 times.
%H Alois P. Heinz, <a href="/A144036/b144036.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p 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);
%t 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_ *)
%Y 4th column of A144042.
%Y Cf. A316104.
%K eigen,nonn
%O 0,4
%A _Alois P. Heinz_, Sep 07 2008
|
