A144036 Shifts left when Euler transform applied 4 times.

0, 1, 1, 5, 19, 89, 410, 2052, 10440, 54874, 293549, 1597621, 8807766, 49107289, 276358791, 1567866228, 8957204966, 51486464912, 297548288251, 1727856600935, 10076859047404, 58996263573440, 346614270372761, 2042929868812385, 12076076910981403

Offset

0,4

Links

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

N. J. A. Sloane, Transforms

Maple

k:=4: 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

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, 4], {n, 0, 30} ] (* Jean-François Alcover, Mar 05 2015, after Alois P. Heinz *)

Crossrefs

4th column of A144042.

Cf. A316104.

Sequence in context: A340994 A301702 A296162 * A110210 A244899 A147139

Adjacent sequences: A144033 A144034 A144035 * A144037 A144038 A144039

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 07 2008

Status

approved