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A144041 Shifts left when Euler transform applied 9 times.

%I A144041 #14 Jun 25 2018 09:32:55
%S A144041 0,1,1,10,64,529,4270,37078,328765,2997844,27840748,262746590,
%T A144041 2511753957,24274552279,236771528856,2327857190814,23045073461778,
%U A144041 229523320443974,2298252776303916,23122596000124215,233629865440550370,2369682121825700424,24119295413989862382
%N A144041 Shifts left when Euler transform applied 9 times.
%H A144041 Alois P. Heinz, <a href="/A144041/b144041.txt">Table of n, a(n) for n = 0..960</a>
%H A144041 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p A144041 k:=9: 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 A144041 k = 9; 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 A144041 9th column of A144042.
%Y A144041 Cf. A316109.
%K A144041 eigen,nonn
%O A144041 0,4
%A A144041 _Alois P. Heinz_, Sep 07 2008