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A144039 Shifts left when Euler transform applied 7 times.

%I A144039 #14 Jun 24 2018 20:28:24
%S A144039 0,1,1,8,43,295,1982,14379,106464,811769,6304231,49770106,398042059,
%T A144039 3218655532,26269422252,216121646661,1790428656802,14922986525284,
%U A144039 125050910828179,1052916751167676,8903502888220215,75579379572985970,643818145873489913
%N A144039 Shifts left when Euler transform applied 7 times.
%H A144039 Alois P. Heinz, <a href="/A144039/b144039.txt">Table of n, a(n) for n = 0..1000</a>
%H A144039 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p A144039 k:=7: 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 A144039 k = 7; 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]; b[1] = etr[a]; For[t = 2, t <= k, t++, b[t] = etr[b[t-1]]]; a[n_] := If[n<2, n, b[k][n-1]]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 09 2015, after _Alois P. Heinz_ *)
%Y A144039 7th column of A144042.
%Y A144039 Cf. A316107.
%K A144039 eigen,nonn
%O A144039 0,4
%A A144039 _Alois P. Heinz_, Sep 07 2008