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Search: id:A013988
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| A013988 |
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Triangle of numbers related to triangle A049224; generalization of Stirling numbers of second kind A008277, Bessel triangle A001497. |
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4
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| 1, 5, 1, 55, 15, 1, 935, 295, 30, 1, 21505, 7425, 925, 50, 1, 623645, 229405, 32400, 2225, 75, 1, 21827575, 8423415, 1298605, 103600, 4550, 105, 1, 894930575, 358764175, 59069010, 5235405, 271950, 8330, 140, 1, 42061737025, 17398082625
(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(-5; 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)= A008543(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!*A049224(n, m)/(m!*6^(n-m)); a(n+1, m) = (6*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-(1-6*x)^(1/6))^m)/m!.
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EXAMPLE
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{1}; {5,1}; {55,15,1}; {935,295,30,1}; {21505,7425,925,50,1}; ...
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CROSSREFS
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Cf. A004747, A000369, A011801, A028844.
Sequence in context: A048897 A049029 A051150 this_sequence A050970 A138548 A113114
Adjacent sequences: A013985 A013986 A013987 this_sequence A013989 A013990 A013991
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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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