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%I #12 May 09 2021 12:58:25
%S 1,3,23,294,5194,116620,3175717,101696700,3745365444,155975005998,
%T 7247927859875,371803988506742,20870023274690966,1272424816703533792,
%U 83736949788656865729,5916106654032037435800,446636583718649775483144,35882981062654529341219962,3056767877633271802374850239
%N a(n) = Sum_{k = 0..n} n! * LaguerreL(n, -k).
%F a(n) = (-1)^n * Sum_{k=0..n} KummerU(-n, 1, -k).
%F a(n) = n! * Sum_{m=0..n} Sum_{j=0..n} binomial(n, j) * m^j / j!.
%F a(n) ~ exp(n/phi - n) * phi^(2*n+1) * n^n / (5^(1/4) * (1 - exp(-1/phi))), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, May 09 2021
%t a[n_] := Sum[n! LaguerreL[n, -k], {k, 0, n}];
%t Table[a[n], {n, 0, 18}]
%o (PARI)
%o a(n) = n!*sum(m=0, n, sum(j=0, n, binomial(n, j) * m^j / j!))
%o for(n=0, 18, print(a(n)))
%Y Cf. A277373, A343848, A344106, A344107.
%K nonn
%O 0,2
%A _Peter Luschny_, May 08 2021