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A144038 Shifts left when Euler transform applied 6 times.

%I A144038 #13 Jun 24 2018 19:45:35
%S A144038 0,1,1,7,34,209,1260,8219,54677,374904,2617996,18588586,133708072,
%T A144038 972484206,7139186644,52832157095,393700752053,2951755132720,
%U A144038 22250074031893,168524281244364,1281906305775734,9788771511218660,75010092629043843,576625427728255451
%N A144038 Shifts left when Euler transform applied 6 times.
%H A144038 Alois P. Heinz, <a href="/A144038/b144038.txt">Table of n, a(n) for n = 0..1000</a>
%H A144038 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p A144038 k:=6: 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 A144038 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, 6], {n, 0, 30} ] (* _Jean-François Alcover_, Mar 05 2015, after _Alois P. Heinz_ *)
%Y A144038 6th column of A144042.
%Y A144038 Cf. A316106.
%K A144038 eigen,nonn
%O A144038 0,4
%A A144038 _Alois P. Heinz_, Sep 07 2008