A144035 Shifts left when Euler transform applied 3 times.

0, 1, 1, 4, 13, 51, 197, 828, 3526, 15538, 69627, 317564, 1466868, 6853320, 32317354, 153636769, 735493374, 3542610091, 17155811156, 83480667707, 407969449010, 2001479974330, 9853652529076, 48666276924852, 241059431701113, 1197237945360797, 5960804381552300

Offset: 0

Author

Alois P. Heinz, Sep 07 2008

Keywords

• eigen
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms

Crossrefs

3rd column of A144042.

Cf. A316103.

Programs

Maple

b:= ((proc(p) local b; b:= proc(n) option remember; `if`(n=0, 1,
        add(add(d*p(d), d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
      end end)@@3)(a):
a:= n-> b(n-1):
seq(a(n), n=0..25);  # revised Alois P. Heinz, Aug 27 2018

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