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A350855 a(0) = 1, a(n) = (n+1)*a(n-1) + (n-2).

%I A350855 #28 Feb 03 2025 19:17:48
%S A350855 1,1,3,13,67,405,2839,22717,204459,2044597,22490575,269886909,
%T A350855 3508529827,49119417589,736791263847,11788660221565,200407223766619,
%U A350855 3607330027799157,68539270528183999,1370785410563679997,28786493621837279955,633302859680420159029,14565965772649663657687
%N A350855 a(0) = 1, a(n) = (n+1)*a(n-1) + (n-2).
%H A350855 Harvey P. Dale, <a href="/A350855/b350855.txt">Table of n, a(n) for n = 0..449</a>
%F A350855 a(n) ~ (6-2e)*(n+1)!.
%F A350855 E.g.f.: (exp(x)*(4*x-x^2-5)+6)/(x-1)^2. - _Alois P. Heinz_, Jan 19 2022
%e A350855 a(1) = (1+1)*a(0) + (1-2) = 2-1 = 1.
%e A350855 a(2) = (2+1)*a(1) + (2-2) = 3.
%t A350855 Nest[Append[#1, (#2 + 1) #1[[-1]] + (#2 - 2)] & @@ {#, Length@ #} &, {1}, 20] (* _Michael De Vlieger_, Jan 19 2022 *)
%t A350855 nxt[{n_,a_}]:={n+1,a(n+2)+n-1}; NestList[nxt,{0,1},30][[;;,2]] (* _Harvey P. Dale_, Feb 03 2025 *)
%o A350855 (PARI) a(n) = if (n, (n+1)*a(n-1) + (n-2), 1); \\ _Michel Marcus_, Jan 19 2022
%o A350855 (Python)
%o A350855 terms = [1]
%o A350855 for n in range(1, 20):
%o A350855     terms.append((n+1)*terms[-1]+n-2)
%o A350855 print(terms) # _Gleb Ivanov_, Jan 19 2022
%Y A350855 Cf. A020543.
%K A350855 nonn
%O A350855 0,3
%A A350855 _Amrit Awasthi_, Jan 19 2022