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A144040 Shifts left when Euler transform applied 8 times.

%I A144040 #14 Jun 25 2018 10:02:32
%S A144040 0,1,1,9,53,401,2967,23659,192615,1613687,13769538,119419761,
%T A144040 1049154071,9318828138,83541286988,754920397795,6869170162829,
%U A144040 62884110339333,578768613062948,5352307127138701,49708821972158231,463445557084360740,4335898935627480699
%N A144040 Shifts left when Euler transform applied 8 times.
%H A144040 Alois P. Heinz, <a href="/A144040/b144040.txt">Table of n, a(n) for n = 0..1000</a>
%H A144040 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p A144040 k:=8: 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 A144040 k = 8; 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 A144040 8th column of A144042.
%Y A144040 Cf. A316108.
%K A144040 eigen,nonn
%O A144040 0,4
%A A144040 _Alois P. Heinz_, Sep 07 2008