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