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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

Table of n, a(n) for n=1..55.

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.)