

A111924


Triangle of Bessel numbers read by rows. Row n gives T(n,n), T(n,n1), T(n,n2), ..., T(n,1) for n >= 1.


9



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, 28, 210, 420, 105, 0, 0, 0, 1, 36, 378, 1260, 945, 0, 0, 0, 0, 1, 45, 630, 3150, 4725, 945, 0, 0, 0, 0, 1, 55, 990, 6930, 17325, 10395, 0, 0, 0, 0, 0, 1, 66, 1485, 13860, 51975, 62370
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OFFSET

1,5


COMMENTS

T(n,k) = number of partitions of an nset into k nonempty subsets, each of size at most 2.


REFERENCES

J. Y. Choi and J. D. H. Smith, On the unimodality and combinatorics of Bessel numbers, Discrete Math., 264 (2003), 4553.


LINKS

Table of n, a(n) for n=1..72.


FORMULA

The ChoiSmith reference gives many further properties and formulas.
T(n, k) = T(n1, k1) + (n1)*T(n2, k1).


EXAMPLE

Triangle begins:
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 28 210 420 105 0 0 0
1 36 378 1260 945 0 0 0 0


MATHEMATICA

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 *)


CROSSREFS

A100861 is another version of this triangle. Row sums give A000085.
Sequence in context: A129684 A247255 A105147 * A212880 A211510 A243984
Adjacent sequences: A111921 A111922 A111923 * A111925 A111926 A111927


KEYWORD

nonn,tabl,easy


AUTHOR

N. J. A. Sloane, Nov 25 2005


EXTENSIONS

More terms from Robert G. Wilson v, Dec 09 2005


STATUS

approved



