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 A049404 Triangle read by rows, the Bell transform of n!*binomial(2,n) (without column 0). 8
 1, 2, 1, 2, 6, 1, 0, 20, 12, 1, 0, 40, 80, 20, 1, 0, 40, 360, 220, 30, 1, 0, 0, 1120, 1680, 490, 42, 1, 0, 0, 2240, 9520, 5600, 952, 56, 1, 0, 0, 2240, 40320, 48720, 15120, 1680, 72, 1, 0, 0, 0, 123200, 332640, 184800, 35280, 2760, 90, 1, 0, 0, 0, 246400, 1786400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was: A triangle of numbers related to triangle A049324. a(n,1) = A008279(2,n-1). a(n,m) =: S1(-2; n,m), a member of a sequence of lower triangular Jabotinsky matrices, including S1(1; n,m) = A008275 (signed Stirling first kind), S1(2; n,m) = A008297(n,m) (signed Lah numbers). a(n,m) matrix is inverse to signed matrix ((-1)^(n-m))*A004747(n,m). The monic row polynomials E(n,x) := sum(a(n,m)*x^m,m=1..n), E(0,x) := 1 are exponential convolution polynomials (see A039692 for the definition and a Knuth reference). For the definition of the Bell transform see A264428 and the link. - Peter Luschny, Jan 16 2016 LINKS W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4. W. Lang, First 10 rows of the array and more. [From Wolfdieter Lang, Oct 17 2008] Peter Luschny, The Bell transform FORMULA a(n, m) = n!*A049324(n, m)/(m!*3^(n-m)); a(n, m) = (3*m-n+1)*a(n-1, m) + a(n-1, m-1), n >= m >= 1; a(n, m) = 0, n

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Last modified July 14 03:42 EDT 2020. Contains 335716 sequences. (Running on oeis4.)