A144819 Shifts left when Dirichlet convolution with a (DC:(b,a)->c) applied 5 times.

1, 1, 6, 36, 231, 1386, 8496, 50976, 306956, 1842276, 11060586, 66363516, 398229516, 2389377096, 14336517456, 86019146316, 516116428791, 3096698572746, 18580200896796, 111481205380776, 668887287816276

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Maple

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:= proc(n, k) local a, b, t; b[1]:= dc(a, a); for t from 2 to k do b[t]:= dc(b[t-1], a) od: a:= n-> `if`(n=1, 1, b[k](n-1)); a(n) end: a:= n-> A(n, 5): seq (a(n), n=1..30);

Mathematica

dc[b_, c_] := Module[{f}, f[n_] := f[n] = Sum[b[d] c[n/d], {d, If[n<0, {}, Divisors[n]]}]; f];
A[n_, k_] := Module[{a, b, t}, b[1] = dc[a, a]; For[t = 2, t <= k, t++, b[t] = dc[b[t-1], a]]; a = Function[m, If[m==1, 1, b[k][m-1]]]; a[n]];
a[n_] := A[n, 5];
Array[a, 30] (* Jean-François Alcover, Dec 18 2020, after Maple *)

Crossrefs

5th column of A144823.

Sequence in context: A129327 A244889 A344269 * A284647 A099252 A057395

Adjacent sequences: A144816 A144817 A144818 * A144820 A144821 A144822

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 21 2008

Status

approved