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 A049424 Triangle read by rows, the Bell transform of n!*binomial(4,n) (without column 0). 3
 1, 4, 1, 12, 12, 1, 24, 96, 24, 1, 24, 600, 360, 40, 1, 0, 3024, 4200, 960, 60, 1, 0, 12096, 40824, 17640, 2100, 84, 1, 0, 36288, 338688, 270144, 55440, 4032, 112, 1, 0, 72576, 2407104, 3580416, 1212624, 144144, 7056, 144, 1, 0, 72576, 14515200, 41791680 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was: A triangle of numbers related to triangle A049326. a(n,1) = A008279(4,n-1). a(n,m) =: S1(-4; 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))*A011801(n,m). The monic row polynomials E(n,x) := Sum_{m=1..n} a(n,m)*x^m, 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. Peter Luschny, The Bell transform FORMULA a(n, m) = n!*A049326(n, m)/(m!*5^(n-m)); a(n, m) = (5*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 May 18 06:33 EDT 2021. Contains 343994 sequences. (Running on oeis4.)