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CONTINUANT transform of {d(n)}, 1, 2, 2, 3, 2, 4, ... (A000005).
1

%I #14 Nov 20 2024 15:16:45

%S 1,3,7,24,55,244,543,2416,7791,33580,74951,483286,1041523,4649378,

%T 19639035,102844553,225328141,1454813399,3134954939,20264543033,

%U 84193127071,357037051317,798267229705,6743174888957,21027791896576,90854342475261,384445161797620

%N CONTINUANT transform of {d(n)}, 1, 2, 2, 3, 2, 4, ... (A000005).

%H Alois P. Heinz, <a href="/A071108/b071108.txt">Table of n, a(n) for n = 1..500</a>

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

%p with(numtheory):

%p a:= proc(n) option remember; `if`(n<0, 0,

%p `if`(n=0, 1, tau(n) *a(n-1) +a(n-2)))

%p end:

%p seq(a(n), n=1..35); # _Alois P. Heinz_, Aug 06 2013

%t a[n_] := a[n] = If[n < 0, 0, If[n == 0, 1, DivisorSigma[0, n]*a[n-1] + a[n-2]]];

%t Table[a[n], { n, 1, 35}] (* _Jean-François Alcover_, Nov 20 2024, after _Alois P. Heinz_ *)

%Y Cf. A000005.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 11 2002