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A379612 a(n) = (n + 1)^(n - 1) + (n + 1)^(n - 2), by convention a(1) = 1.

%I A379612 #12 Mar 19 2025 09:03:21
%S A379612 2,1,4,20,150,1512,19208,294912,5314410,110000000,2572306572,
%T A379612 67077144576,1930018885886,60743477544960,2075941406250000,
%U A379612 76561193665298432,3030800878069216722,128186171713071710208,5768828271352423353620,275251200000000000000000,13879377432727741655370342
%N A379612 a(n) = (n + 1)^(n - 1) + (n + 1)^(n - 2), by convention a(1) = 1.
%H A379612 G. C. Greubel, <a href="/A379612/b379612.txt">Table of n, a(n) for n = 0..385</a>
%F A379612 a(n) = (n + 2)*(n + 1)^(n - 2) if n != 1.
%F A379612 E.g.f.: (-1/(2*x))*( (W(-x) + 2)^2 + x^2 - 4 ), W(x) = Lambert W function. - _G. C. Greubel_, Mar 18 2025
%p A379612 a := n -> ifelse(n=1, 1, (n + 1)^(n - 1) + (n + 1)^(n - 2)): seq(a(n), n = 0..20);
%t A379612 Table[If[n == 1, 1, (n + 1)^(n - 1) + (n + 1)^(n - 2)], {n, 0, 20}] (* _Michael De Vlieger_, Dec 27 2024 *)
%o A379612 (Magma)
%o A379612 A379612:= func< n | n le 1 select 2-n else (n+2)*(n+1)^(n-2) >;
%o A379612 [A379612(n): n in [0..30]]; // _G. C. Greubel_, Mar 18 2025
%o A379612 (SageMath)
%o A379612 def A379612(n): return 2-n if n<2 else (n+2)*(n+1)^(n-2)
%o A379612 print([A379612(n) for n in range(31)]) # _G. C. Greubel_, Mar 18 2025
%Y A379612 Cf. A379611.
%K A379612 nonn
%O A379612 0,1
%A A379612 _Peter Luschny_, Dec 27 2024