A144818 Shifts left when Dirichlet convolution with a (DC:(b,a)->c) applied 4 times.

1, 1, 5, 25, 135, 675, 3475, 17375, 87385, 437175, 2188575, 10942875, 54730525, 273652625, 1368332625, 6841676625, 34208737630, 171043688150, 855220256700, 4276101283500, 21380515232550, 106902576510250, 534512926322750

Offset: 1

Author

Alois P. Heinz, Sep 21 2008

Keywords

• eigen
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane, Transforms

Crossrefs

4th column of A144823.

Programs

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,4): 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, 4];
Array[a, 30] (* Jean-François Alcover, Dec 18 2020, after Maple *)