A144037 Shifts left when Euler transform applied 5 times.
0, 1, 1, 6, 26, 141, 751, 4337, 25512, 154839, 956877, 6014098, 38292603, 246550449, 1602304287, 10497348917, 69253008919, 459673679526, 3067621127220, 20570132531365, 138528107124822, 936524246563021, 6353624897677005, 43242243814689566, 295161330408772329
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..400
- N. J. A. Sloane, Transforms
Programs
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Maple
k:=5: 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);
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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, 5], {n, 0, 30} ] (* Jean-François Alcover, Mar 05 2015, after Alois P. Heinz *)