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A102610 Triangle read by rows: coefficients of characteristic polynomials of lower triangular matrix of Robbins triangle numbers. 0
0, 1, -1, 1, -2, 1, 1, -4, 5, -2, 1, -11, 33, -37, 14, 1, -53, 495, -1423, 1568, -588, 1, -482, 23232, -213778, 612035, -673260, 252252, 1, -7918, 3607384, -172966930, 1590265243, -4551765520, 5006613612, -1875745872, 1, -226266, 1732486848, -787838048562, 37768573496883, -347235787044084 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Roots of n-th characteristic polynomial are the first n Robbins numbers (A005130).

Second column of triangle is partial sums of Robbins numbers negated (A173312).

LINKS

Table of n, a(n) for n=0..41.

EXAMPLE

Generation of the triangle:

We begin with A048601

1

1 1

2 3 2

7 14 14 7

42 105 135 105 42

...

and get polynomials

x - 1

x^2 - 2*x + 1

x^3 - 4*x^2 + 5*x - 2

x^4 - 11*x^3 + 33*x^2 - 37*x + 14

x^5 - 53*x^4 + 495*x^3 - 1423*x^2 + 1568*x - 588

...

PROG

(PARI) T(n, k) = binomial(n+k-2, k-1)*((2*n-k-1)!/(n-k)!)*prod(j=0, n-2, ((3*j+1)!/(n+j)!)) RM(n)=M=matrix(n, n); for(l=1, n, for(k=1, l, M[l, k]=T(l, k))); M for(i=1, 10, print(charpoly(RM(i))))

CROSSREFS

Cf. A005130, A048601.

Sequence in context: A158472 A198895 A118686 * A203300 A134172 A208061

Adjacent sequences:  A102607 A102608 A102609 * A102611 A102612 A102613

KEYWORD

sign,tabl

AUTHOR

Lambert Klasen (lambert.klasen(AT)gmx.net) and Gary W. Adamson, Jan 30 2005

EXTENSIONS

Sequence has been prepended with a(0)=0 to enable table display (so offset has been set to 0 accordingly) by Michel Marcus, Aug 23 2013

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)