A144039 Shifts left when Euler transform applied 7 times.

0, 1, 1, 8, 43, 295, 1982, 14379, 106464, 811769, 6304231, 49770106, 398042059, 3218655532, 26269422252, 216121646661, 1790428656802, 14922986525284, 125050910828179, 1052916751167676, 8903502888220215, 75579379572985970, 643818145873489913

Offset

0,4

Links

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

N. J. A. Sloane, Transforms

Maple

k:=7: 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 = 7; 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

7th column of A144042.

Cf. A316107.

Sequence in context: A111365 A199321 A346198 * A282189 A210125 A044110

Adjacent sequences: A144036 A144037 A144038 * A144040 A144041 A144042

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 07 2008

Status

approved