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A049424
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A triangle of numbers related to triangle A049326.
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3
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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(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).
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LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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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<m; a(n, 0) := 0; a(1, 1)=1. E.g.f. for m-th column: (((-1+(1+x)^5)/5)^m)/m!.
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EXAMPLE
| {1}; {4,1}; {12,12,1}; {24,96,24,1};... E.g. row polynomial E(3,x)= 12*x+12*x^2+x^3.
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CROSSREFS
| Row sums give A049427.
Sequence in context: A051290 A125105 A144878 * A157394 A078219 A187541
Adjacent sequences: A049421 A049422 A049423 * A049425 A049426 A049427
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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