This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343849 #12 May 09 2021 12:58:25
%S A343849 1,3,23,294,5194,116620,3175717,101696700,3745365444,155975005998,
%T A343849 7247927859875,371803988506742,20870023274690966,1272424816703533792,
%U A343849 83736949788656865729,5916106654032037435800,446636583718649775483144,35882981062654529341219962,3056767877633271802374850239
%N A343849 a(n) = Sum_{k = 0..n} n! * LaguerreL(n, -k).
%F A343849 a(n) = (-1)^n * Sum_{k=0..n} KummerU(-n, 1, -k).
%F A343849 a(n) = n! * Sum_{m=0..n} Sum_{j=0..n} binomial(n, j) * m^j / j!.
%F A343849 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 A343849 a[n_] := Sum[n! LaguerreL[n, -k], {k, 0, n}];
%t A343849 Table[a[n], {n, 0, 18}]
%o A343849 (PARI)
%o A343849 a(n) = n!*sum(m=0, n, sum(j=0, n, binomial(n, j) * m^j / j!))
%o A343849 for(n=0, 18, print(a(n)))
%Y A343849 Cf. A277373, A343848, A344106, A344107.
%K A343849 nonn
%O A343849 0,2
%A A343849 _Peter Luschny_, May 08 2021