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a(0) = 1; a(n) = Sum_{k=1..n} gcd(n,k)*a(n-k).
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%I #6 May 28 2019 17:28:25

%S 1,1,3,7,18,34,104,174,510,1082,2714,4658,16316,25634,71978,169258,

%T 419878,712386,2349160,3773934,11980874,25033510,59450390,104012646,

%U 368769280,625406094,1645569502,3654549058,9504389550,16006708782,55050007424,87063424990

%N a(0) = 1; a(n) = Sum_{k=1..n} gcd(n,k)*a(n-k).

%t a[n_] := a[n] = Sum[GCD[n, k] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 31}]

%Y Cf. A003989, A050873, A072979.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 27 2019