%I #20 Sep 08 2022 08:46:05
%S 0,0,2,12,62,320,1712,9604,56674,351792,2293862,15682216,112179608,
%T 837905016,6522165834,52807401908,443962338894,3869376656384,
%U 34908008426360,325530083655692,3133830448212442,31106728455899128,318009567467999574,3344865730200667832,36161434396223563504
%N a(n) = B(n+2)-3*B(n+1)+B(n), where B(i) are the Bell numbers A000110.
%H Vincenzo Librandi, <a href="/A226506/b226506.txt">Table of n, a(n) for n = 0..200</a>
%H B. Chern, P. Diaconis, D. M. Kane, and R. C. Rhoades, <a href="https://arxiv.org/abs/1304.4309">Closed expressions for averages of set partition statistics</a>, arXiv:1304.4309 [math.CO], 2013.
%t Table[BellB[n+2] - 3 BellB[n+1] + BellB[n], {n, 0, 30}] (* _Vincenzo Librandi_, Jul 16 2013 *)
%t #[[3]]-3#[[2]]+#[[1]]&/@Partition[BellB[Range[0,30]],3,1] (* _Harvey P. Dale_, Aug 26 2021 *)
%o (Magma) [Bell(n+2)-3*Bell(n+1)+Bell(n): n in [0..30]]; // _Vincenzo Librandi_, Jul 16 2013
%Y Cf. A000110.
%Y Cf. A005493, A225591 (see Prop 3.1 (i) in Chern et al. link).
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jun 10 2013