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Search: id:A011801
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| A011801 |
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Triangle of numbers related to triangle A049223; generalization of Stirling numbers of second kind A008277, Bessel triangle A001497. |
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12
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| 1, 4, 1, 36, 12, 1, 504, 192, 24, 1, 9576, 3960, 600, 40, 1, 229824, 100656, 17160, 1440, 60, 1, 6664896, 3048192, 563976, 54600, 2940, 84, 1, 226606464, 107255232, 21095424, 2256576, 142800, 5376, 112, 1, 8837652096, 4302305280, 887785920
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n,m) := S2p(-4; n,m), a member of a sequence of triangles including S2p(-1; n,m) := A001497(n-1,m-1) (Bessel triangle) and ((-1)^(n-m))*S2p(1; n,m) := A008277(n,m) (Stirling 2nd kind). a(n,1)= A008546(n-1).
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LINKS
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W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
Index entries for sequences related to Bessel functions or polynomials
P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.
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FORMULA
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a(n, m) = n!*A049223(n, m)/(m!*5^(n-m)); a(n+1, m) = (5*n-m)*a(n, m) + a(n, m-1), n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0, a(1, 1)=1; E.g.f. of m-th column: ((1-(1-5*x)^(1/5))^m)/m!.
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EXAMPLE
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{1}; {4,1}; {36,12,1}; {504,192,24,1}; {9576,3960,600,40,1}; ...
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CROSSREFS
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Cf. A004747, A000369, A028575.
Sequence in context: A091741 A061036 A144267 this_sequence A092667 A060627 A113101
Adjacent sequences: A011798 A011799 A011800 this_sequence A011802 A011803 A011804
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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