A144317 Shifts left when Dirichlet convolution (DC:(b,b)->a) applied 3 times.

1, 1, 8, 64, 540, 4320, 35008, 280064, 2244152, 17955008, 143670304, 1149362432, 9195171392, 73561371136, 588492929536, 4707943678208, 37663565234758, 301308521878064, 2410468302643136, 19283746421145088, 154269972376667232

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

N. J. A. Sloane, Transforms

Maple

k:=3: with (numtheory): dc:= proc(b, c) proc(n) option remember; add (b(d) *c(n/d), d=`if`(n<0, {}, divisors(n))) end end: a:='a': b[1]:= dc(a, a): for t from 2 to k do b[t]:= dc(b[t-1], b[t-1]) od: a:= n-> `if`(n=1, 1, b[k](n-1)): seq (a(n), n=1..30);

Mathematica

dc[b_, c_] := Module[{proc}, proc[n_] := proc[n] = Sum[b[d]*c[n/d], {d, If[n < 0, {}, Divisors[n]]}]; proc];
A[n_, k_] := Module[{a, b, t}, b[1] = dc[a, a]; For[t = 2, t <= k, t++, b[t] = dc[b[t-1], b[t-1]]]; a = Function[m, If[m == 1, 1, b[k][m - 1]]]; a[n]];
a[n_] := A[n, 3];
Array[a, 30] (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *)

Crossrefs

3rd column of A144324, 7th column of A144823.

Sequence in context: A033144 A238300 A344271 * A344054 A344252 A199567

Adjacent sequences: A144314 A144315 A144316 * A144318 A144319 A144320

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 17 2008

Status

approved