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%I #14 Nov 27 2016 07:01:28
%S 0,1,4,18,236,12760,3162582,5965957900,147395915019656,
%T 38431930179989653632,90116582088416163834417290,
%U 2118032070086776060232851050813004,966490912699216393489571072350268614425420,17165261065730992639912668446254005264689353839299152
%N a(n) = Sum_{t=1..n} binomial(n,t)*t^(1+(n-t)^2).
%H Daniel J. Kleitman, Bruce L. Rothschild and Joel H. Spencer, <a href="https://doi.org/10.1090/S0002-9939-1976-0414380-0">The number of semigroups of order n</a>, Proc. Amer. Math. Soc., 55 (1976), 227-232. See Eq. (1.2).
%t Table[Sum[Binomial[n, t] t^(1 + (n - t)^2), {t, 1, n}], {n, 0, 25}] (* _Vincenzo Librandi_, Nov 27 2016 *)
%Y Cf. A001423.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 25 2016