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%I #20 Nov 14 2023 07:05:05
%S 1,1,6,22,117,705,4972,39916,360105,3606865,39721266,477061026,
%T 6205806061,86925018817,1304396077272,20877063837400,355003736855697,
%U 6391465311099681,121460116022428510,2429579599296960430,51027940329395658981,1122742916106886416001
%N Row sums of triangle A076732.
%C a(n)/ceiling(n/2), i.e., a(n) divided by the positive integers repeated, leads to another sequence of integer numbers [1, 1, 3, 11, 39, 235, 1243, 9979, ... ].
%H Alois P. Heinz, <a href="/A193463/b193463.txt">Table of n, a(n) for n = 1..450</a>
%F a(n) = Sum_{k=1..n} A076732(n,k).
%F a(n) = Sum_{k=1..n} (k/(n-k)!)*A047920(n,k).
%F a(n) = Sum_{k=1..n} (k/(n-k)!) * Sum_{j=0..k-1} (-1)^j*binomial(k-1,j)*(n-1-j)!.
%p A193463:=proc(n): add(A076732(n,k), k=1..n) end: A076732:=proc(n,k): (k/(n-k)!)*A047920(n,k) end: A047920:=proc(n,k): add(((-1)^j)*binomial(k-1,j)*(n-1-j)!, j=0..k-1) end: seq(A193463(n), n=1..22);
%t A000240[n_] := Subfactorial[n] - (-1)^n;
%t T[n_, k_] := T[n, k] = Switch[k, 1, 1, n, A000240[n], _, k*T[n - 1, k - 1] + T[n - 1, k]];
%t a[n_] := Sum[T[n, k], {k, 1, n}];
%t Table[a[n], {n, 1, 22}] (* _Jean-François Alcover_, Nov 14 2023 *)
%Y Cf. A047920, A076732.
%K nonn,easy
%O 1,3
%A _Johannes W. Meijer_, Jul 27 2011
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