A102610 - OEIS

%I #11 Aug 23 2013 07:55:08

%S 0,1,-1,1,-2,1,1,-4,5,-2,1,-11,33,-37,14,1,-53,495,-1423,1568,-588,1,

%T -482,23232,-213778,612035,-673260,252252,1,-7918,3607384,-172966930,

%U 1590265243,-4551765520,5006613612,-1875745872,1,-226266,1732486848,-787838048562,37768573496883,-347235787044084

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

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

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

%e Generation of the triangle:

%e We begin with A048601

%e 1

%e 1 1

%e 2 3 2

%e 7 14 14 7

%e 42 105 135 105 42

%e ...

%e and get polynomials

%e x - 1

%e x^2 - 2*x + 1

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

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

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

%e ...

%o (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))))

%Y Cf. A005130, A048601.

%K sign,tabl

%O 0,5

%A Lambert Klasen (lambert.klasen(AT)gmx.net) and _Gary W. Adamson_, Jan 30 2005

%E 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