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A305465 a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*n^(n-2*k).

%I A305465 #17 Sep 22 2019 09:07:59
%S A305465 1,1,9,174,6433,387045,34372513,4223468872,685727920641,
%T A305465 142133068151865,36615156774045001,11474421446955693006,
%U A305465 4298048476279871328289,1896322606147540294800349,973319784969445114237699713,575000041101937659730069884960
%N A305465 a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*n^(n-2*k).
%H A305465 Seiichi Manyama, <a href="/A305465/b305465.txt">Table of n, a(n) for n = 0..232</a>
%F A305465 a(n) ~ n! * n^n. - _Vaclav Kotesovec_, Jun 03 2018
%t A305465 Join[{1},Table[Sum[(n-k)!/k! Binomial[n-k,k]n^(n-2k),{k,0,Floor[n/2]}],{n,20}]] (* _Harvey P. Dale_, Sep 22 2019 *)
%o A305465 (PARI) {a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*n^(n-2*k))}
%Y A305465 Main diagonal of A305401.
%Y A305465 Cf. A021009, A305467.
%K A305465 nonn
%O A305465 0,3
%A A305465 _Seiichi Manyama_, Jun 02 2018