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A144366 Shifts 2 places left under Dirichlet convolution.

%I A144366 #16 Feb 18 2024 10:10:18
%S A144366 1,1,1,2,2,5,4,12,8,28,17,60,34,134,68,276,140,580,280,1186,560,2436,
%T A144366 1128,4906,2256,9976,4516,20020,9048,40324,18096,80860,36192,162320,
%U A144366 72418,324920,144852,651177,289704,1302914,579476,2608360,1158952
%N A144366 Shifts 2 places left under Dirichlet convolution.
%C A144366 Appears to be essentially the same as a sequence in Section 2.2 of Baril-Ramirez. - _N. J. A. Sloane_, Feb 18 2024
%H A144366 Alois P. Heinz, <a href="/A144366/b144366.txt">Table of n, a(n) for n = 1..1000</a>
%H A144366 Jean-Luc Baril and José L. Ramírez, <a href="http://jl.baril.u-bourgogne.fr/knight.pdf">Knight's paths towards Catalan numbers</a>, Univ. Bourgogne Franche-Comté (2022). Also arXiv:2206.12087, Jan 2023.
%H A144366 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A144366 G.f.: x + x^2 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - _Ilya Gutkovskiy_, May 09 2019
%p A144366 k:= 2: with(numtheory): dck:= proc(b,c) proc(n, k) option remember; add(b(d,k) *c(n/d,k), d=`if`(n<0,{}, divisors(n))) end end: B:= dck(T,T): T:= (n, k)-> if n<=k then 1 else B(n-k, k) fi: a:= n-> T(n,k): seq(a(n), n=1..50);
%t A144366 k = 2; dck[b_, c_][n_, k_] := dck[b, c][n, k] = DivisorSum[n, b[#, k] * c[n/#, k]&]; B = dck[T, T]; T[n_, k_] :=  If[n <= k, 1, B[n-k, k]]; a[n_] := T[n, k]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Apr 05 2017, translated from Maple *)
%Y A144366 2nd column of A144374. Cf. A000005.
%K A144366 eigen,nonn
%O A144366 1,4
%A A144366 _Alois P. Heinz_, Sep 18 2008