A102610 Triangle read by rows: coefficients of characteristic polynomials of lower triangular matrix of Robbins triangle numbers.

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

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: A355635 A118686 A355540 * 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