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A329966 a(n) = n! * Sum_{d|n} binomial(n-1,d-1) / d!.

%I A329966 #13 Sep 08 2022 08:46:24
%S A329966 1,3,7,61,121,3721,5041,240241,2056321,23768641,39916801,11104853761,
%T A329966 6227020801,683519316481,32048919302401,577844178912001,
%U A329966 355687428096001,261396772808371201,121645100408832001,202418558674082150401,2061884451929702400001,12935940353987812761601
%N A329966 a(n) = n! * Sum_{d|n} binomial(n-1,d-1) / d!.
%H A329966 Robert Israel, <a href="/A329966/b329966.txt">Table of n, a(n) for n = 1..447</a>
%p A329966 N:= 30:
%p A329966 V:= Vector(N):
%p A329966 for d from 1 to N do
%p A329966    for k from 1 to floor(N/d) do
%p A329966      n:= k*d; V[n]:= V[n] + n!/d!*binomial(n-1,d-1);
%p A329966 od od:
%p A329966 convert(V,list); # _Robert Israel_, Jan 01 2020
%t A329966 a[n_] := n! Sum[Binomial[n - 1, d - 1]/d!, {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]
%o A329966 (PARI) a(n) = n! * sumdiv(n, d, binomial(n-1,d-1) / d!); \\ _Michel Marcus_, Nov 26 2019
%o A329966 (Magma) [Factorial(n)*( &+[ Binomial(n-1,d-1)/Factorial(d):d in Divisors(n)]): n in [1..22]]; // _Marius A. Burtea_, Jan 02 2020
%Y A329966 Cf. A000262, A056045, A057625, A271654.
%K A329966 nonn
%O A329966 1,2
%A A329966 _Ilya Gutkovskiy_, Nov 26 2019