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Search: id:A080417
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| A080417 |
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Signed Stirling numbers of the second kind. |
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+0
1
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| 1, 1, -1, 1, -3, 1, 1, -7, 6, -1, 1, -15, 25, -10, 1, 1, -31, 90, -65, 15, -1, 1, -63, 301, -350, 140, -21, 1, 1, -127, 966, -1701, 1050, -266, 28, -1, 1, -255, 3025, -7770, 6951, -2646, 462, -36, 1, 1, -511, 9330, -34105, 42525, -22827, 5880, -750, 45, -1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Define (n+1) X (n+1) matrices by M(n)=(binomial(i+1,j),i,j=0..n). The coefficients of the characteristic polynomials of these matrices yield the above sequence. Note : first 1 added to complete the triangle.
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FORMULA
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T(1, 1)=1, T(1, k)=0, k>1. T(n, k)=-T(n-1, k-1)+kT(n, k-1), n>1
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EXAMPLE
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Rows are {1}, {1,-1}, {1,-3,1},{1,-7,6,-1},{1,-15,25,-10,1},... 25=-(-7)+3*6, -10=-6+4(-1)
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CROSSREFS
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Cf. A008277.
Sequence in context: A130749 A154959 A008277 this_sequence A133800 A146900 A132733
Adjacent sequences: A080414 A080415 A080416 this_sequence A080418 A080419 A080420
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 18 2003
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