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A049411
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A triangle of numbers related to triangle A049327.
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3
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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).
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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!*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<m; a(n, 0) := 0; a(1, 1)=1. E.g.f. for m-th column: (((-1+(1+x)^6)/6)^m)/m!.
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EXAMPLE
| {1}; {5,1}; {20,15,1}; {60,155,30,1};... E.g. row polynomial E(3,x)= 20*x+15*x^2+x^3.
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CROSSREFS
| Row sums give A049428.
Sequence in context: A088577 A127561 A144879 * A070729 A101693 A063476
Adjacent sequences: A049408 A049409 A049410 * A049412 A049413 A049414
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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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