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A144035 Shifts left when Euler transform applied 3 times. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

N. J. A. Sloane, Transforms

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-Fran├žois Alcover, Mar 05 2015, after Alois P. Heinz *)

CROSSREFS

3rd column of A144042.

Cf. A316103.

Sequence in context: A300122 A149461 A056276 * A056277 A082951 A135345

Adjacent sequences:  A144032 A144033 A144034 * A144036 A144037 A144038

KEYWORD

eigen,nonn

AUTHOR

Alois P. Heinz, Sep 07 2008

STATUS

approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)