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A343848 a(n) = Sum_{k = 0..n} (n - k)! LaguerreL(n - k, -k).

%I A343848 #7 May 09 2021 08:04:17
%S A343848 1,2,5,17,77,444,3123,25933,248163,2687200,32460889,432482545,
%T A343848 6296217017,99388128516,1690073020687,30788225809509,597998944638879,
%U A343848 12332575195452440,269072563350272149,6190949611140562505,149789737789559221397,3801359947725801283196
%N A343848 a(n) = Sum_{k = 0..n} (n - k)! LaguerreL(n - k, -k).
%F A343848 a(n) = Sum_{k=0..n} (n - k)! * Sum_{j=0..n-k} binomial(n - k, j) * k^j / j!.
%p A343848 A343848List := proc(n) local T; T := proc(n, k) option remember;
%p A343848 if n = k then return 1 elif n = k+1 then return k+1 fi;
%p A343848 (2*n-k-1)*T(n-1, k) - (n-k-1)^2*T(n-2, k) end:
%p A343848 seq(add(T(k, j), j = 0..k), k = 0..n) end: A343848List(21);
%t A343848 a[n_] := Sum[(n - k)! LaguerreL[n - k, -k], {k, 0, n}];
%t A343848 Table[a[n], {n, 0, 21}]
%o A343848 (PARI)
%o A343848 a(n) = sum(k=0, n, (n - k)!*sum(j=0, n - k, binomial(n - k, j) * k^j / j!))
%o A343848 for(n=0, 21, print(a(n)))
%Y A343848 Row sums of A343847.
%K A343848 nonn
%O A343848 0,2
%A A343848 _Peter Luschny_, May 08 2021