A144040 Shifts left when Euler transform applied 8 times.

0, 1, 1, 9, 53, 401, 2967, 23659, 192615, 1613687, 13769538, 119419761, 1049154071, 9318828138, 83541286988, 754920397795, 6869170162829, 62884110339333, 578768613062948, 5352307127138701, 49708821972158231, 463445557084360740, 4335898935627480699

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Maple

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);

Mathematica

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 *)

Crossrefs

8th column of A144042.

Cf. A316108.

Sequence in context: A038761 A003698 A001688 * A336184 A326606 A052108

Adjacent sequences: A144037 A144038 A144039 * A144041 A144042 A144043

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 07 2008

Status

approved