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%I #19 Aug 27 2018 22:43:46
%S 0,1,1,4,13,51,197,828,3526,15538,69627,317564,1466868,6853320,
%T 32317354,153636769,735493374,3542610091,17155811156,83480667707,
%U 407969449010,2001479974330,9853652529076,48666276924852,241059431701113,1197237945360797,5960804381552300
%N Shifts left when Euler transform applied 3 times.
%H Alois P. Heinz, <a href="/A144035/b144035.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p b:= ((proc(p) local b; b:= proc(n) option remember; `if`(n=0, 1,
%p add(add(d*p(d), d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
%p end end)@@3)(a):
%p a:= n-> b(n-1):
%p seq(a(n), n=0..25); # revised _Alois P. Heinz_, Aug 27 2018
%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, 3], {n, 0, 30} ] (* _Jean-François Alcover_, Mar 05 2015, after _Alois P. Heinz_ *)
%Y 3rd column of A144042.
%Y Cf. A316103.
%K eigen,nonn
%O 0,4
%A _Alois P. Heinz_, Sep 07 2008