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 A013988 Triangle read by rows, the inverse Bell transform of n!*binomial(5,n) (without column 0). 9
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was: Triangle of numbers related to triangle A049224; generalization of Stirling numbers of second kind A008277, Bessel triangle A001497. 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). For the definition of the Bell transform see A264428 and the link. - Peter Luschny, Jan 16 2016 LINKS P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, arXiv:quant-ph/0402027, 2004. M. Janjic, Some classes of numbers and derivatives, JIS 12 (2009) 09.8.3 W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4. Peter Luschny, The Bell transform FORMULA 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

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Last modified May 16 19:46 EDT 2021. Contains 343951 sequences. (Running on oeis4.)