A144041 Shifts left when Euler transform applied 9 times.
0, 1, 1, 10, 64, 529, 4270, 37078, 328765, 2997844, 27840748, 262746590, 2511753957, 24274552279, 236771528856, 2327857190814, 23045073461778, 229523320443974, 2298252776303916, 23122596000124215, 233629865440550370, 2369682121825700424, 24119295413989862382
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..960
- N. J. A. Sloane, Transforms
Programs
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Maple
k:=9: 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
k = 9; 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 *)