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 A049411 Triangle read by rows, the Bell transform of n!*binomial(5,n) (without column 0). 3
 1, 5, 1, 20, 15, 1, 60, 155, 30, 1, 120, 1300, 575, 50, 1, 120, 9220, 8775, 1525, 75, 1, 0, 55440, 114520, 36225, 3325, 105, 1, 0, 277200, 1315160, 730345, 112700, 6370, 140, 1, 0, 1108800, 13428800, 13000680, 3209745, 291060, 11130, 180, 1, 0, 3326400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was: A triangle of numbers related to triangle A049327. a(n,1) = A008279(5,n-1). a(n,m) =: S1(-5; 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))*A013988(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. Peter Luschny, The Bell transform FORMULA a(n, m) = n!*A049327(n, m)/(m!*6^(n-m)); a(n, m) = (6*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 August 6 12:30 EDT 2020. Contains 336246 sequences. (Running on oeis4.)