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A111924 Triangle of Bessel numbers read by rows. Row n gives T(n,n), T(n,n-1), T(n,n-2), ..., T(n,1) for n >= 1.

%I A111924 #10 Jun 16 2016 23:27:29
%S A111924 1,1,1,1,3,0,1,6,3,0,1,10,15,0,0,1,15,45,15,0,0,1,21,105,105,0,0,0,1,
%T A111924 28,210,420,105,0,0,0,1,36,378,1260,945,0,0,0,0,1,45,630,3150,4725,
%U A111924 945,0,0,0,0,1,55,990,6930,17325,10395,0,0,0,0,0,1,66,1485,13860,51975,62370
%N A111924 Triangle of Bessel numbers read by rows. Row n gives T(n,n), T(n,n-1), T(n,n-2), ..., T(n,1) for n >= 1.
%C A111924 T(n,k) = number of partitions of an n-set into k nonempty subsets, each of size at most 2.
%D A111924 J. Y. Choi and J. D. H. Smith, On the unimodality and combinatorics of Bessel numbers, Discrete Math., 264 (2003), 45-53.
%F A111924 The Choi-Smith reference gives many further properties and formulas.
%F A111924 T(n, k) = T(n-1, k-1) + (n-1)*T(n-2, k-1).
%e A111924 Triangle begins:
%e A111924 1
%e A111924 1 1
%e A111924 1 3 0
%e A111924 1 6 3 0
%e A111924 1 10 15 0 0
%e A111924 1 15 45 15 0 0
%e A111924 1 21 105 105 0 0 0
%e A111924 1 28 210 420 105 0 0 0
%e A111924 1 36 378 1260 945 0 0 0 0
%t A111924 T[n_, 0] = 0; T[1, 1] = 1; T[2, 1] = 1; T[n_, k_] := T[n - 1, k - 1] + (n - 1)T[n - 2, k - 1]; Table[T[n, k], {n, 12}, {k, n, 1, -1}] // Flatten (* _Robert G. Wilson v_ *)
%Y A111924 A100861 is another version of this triangle. Row sums give A000085.
%K A111924 nonn,tabl,easy
%O A111924 1,5
%A A111924 _N. J. A. Sloane_, Nov 25 2005
%E A111924 More terms from _Robert G. Wilson v_, Dec 09 2005