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 A080417 Signed Stirling numbers of the second kind. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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. LINKS Russell Merris, The p-Stirling Numbers, Turk J Math, 24 (2000) , 379-399. See p. 3. FORMULA T(1, 1)=1, T(1, k)=0, k>1. T(n, k)=-T(n-1, k-1)+kT(n, k-1), n>1 EXAMPLE 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) CROSSREFS Cf. A008277. Sequence in context: A250118 A250119 A154959 * A008277 A218577 A193387 Adjacent sequences:  A080414 A080415 A080416 * A080418 A080419 A080420 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Feb 18 2003 STATUS approved

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Last modified November 14 14:50 EST 2018. Contains 317208 sequences. (Running on oeis4.)