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A144819 Shifts left when Dirichlet convolution with a (DC:(b,a)->c) applied 5 times. 2


%S 1,1,6,36,231,1386,8496,50976,306956,1842276,11060586,66363516,

%T 398229516,2389377096,14336517456,86019146316,516116428791,

%U 3096698572746,18580200896796,111481205380776,668887287816276

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

%H Alois P. Heinz, <a href="/A144819/b144819.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%p 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);

%t dc[b_, c_] := Module[{f}, f[n_] := f[n] = Sum[b[d] c[n/d], {d, If[n<0, {}, Divisors[n]]}]; f];

%t 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]];

%t a[n_] := A[n, 5];

%t Array[a, 30] (* _Jean-Fran├žois Alcover_, Dec 18 2020, after Maple *)

%Y 5th column of A144823.

%K eigen,nonn

%O 1,3

%A _Alois P. Heinz_, Sep 21 2008

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Last modified June 20 20:15 EDT 2021. Contains 345232 sequences. (Running on oeis4.)