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A049410
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A triangle of numbers related to triangle A049325.
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3
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1, 3, 1, 6, 9, 1, 6, 51, 18, 1, 0, 210, 195, 30, 1, 0, 630, 1575, 525, 45, 1, 0, 1260, 10080, 6825, 1155, 63, 1, 0, 1260, 51660, 71505, 21840, 2226, 84, 1, 0, 0, 207900, 623700, 333585, 57456, 3906, 108, 1, 0, 0, 623700, 4573800, 4293135, 1195425, 131670
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n,1)= A008279(3,n-1). a(n,m)=: S1(-3; 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))*A000369(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!*A049325(n, m)/(m!*4^(n-m)); a(n, m) = (4*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)^4)/4)^m)/m!.
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EXAMPLE
| {1}; {3,1}; {6,9,1}; {6,51,18,1};... E.g. row polynomial E(3,x)= 6*x+9*x^2+x^3.
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CROSSREFS
| Row sums give A049426.
Sequence in context: A103407 A074475 A144877 * A013610 A008573 A089710
Adjacent sequences: A049407 A049408 A049409 * A049411 A049412 A049413
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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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