0,7

The n-th row consists of coefficients of the characteristic polynomial of the adjacency matrix of the complete n-graph.

Triangle of coefficients of det(M(n)) where M(n) is the n X n matrix m(i,j)=x if i=j, m(i,j)=i/j otherwise. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 01 2003

T is an example of the group of matrices outlined in the table in A132382--the associated matrix for rB(0,1). The e.g.f. for the row polynomials is exp(x*t) * exp(x) *(1-x). T(n,k) = Binomial(n,k)* s(n-k) where s = (1,0,-1,-2,-3,...) with an e.g.f. of exp(x)*(1-x) which is the reciprocal of the e.g.f. of A000166. [From Tom Copeland (tcjpn(AT)msn.com), Sep 10 2008]

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 20 2009: (Start) Row sums are: {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,...}. (End)

Norman Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. p. 17.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p.184 problem 3. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 20 2009]

G.f.: (x-n+1)*(x+1)^(n-1) = sum T(n, k)x^k. T(n, k) = (1-n+k)*C(n, k).

k-th column has o.g.f. x^k(1-(k+2)x)/(1-x)^(k+2). k-th row gives coefficients of (x-k)(x+1)^k. - Paul Barry (pbarry(AT)wit.ie), Jan 25 2004

t(n,m)=Coefficiemtslist[Det[Table[If[i == j, x, 1], {i, 1, n}, {j, 1, n}],x] [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 20 2009]

1; 0,1; -1,0,1; -2,-3,0,1; -3,-8,-6,0,1; ...

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 20 2009: (Start)

{1},

{0, 1},

{-1, 0, 1},

{2, -3, 0, 1},

{-3, 8, -6, 0, 1},

{4, -15, 20, -10, 0, 1},

{-5, 24, -45, 40, -15, 0, 1},

{6, -35, 84, -105, 70, -21, 0, 1},

{-7, 48, -140, 224, -210, 112, -28, 0, 1},

{8, -63, 216, -420, 504, -378, 168, -36, 0, 1},

{-9, 80, -315, 720, -1050, 1008, -630, 240, -45, 0, 1} (End)

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 20 2009: (Start)

Clear[M, a, n, m, i, j];

M[n_] := Table[If[i == j, x, 1], {i, 1, n}, {j, 1, n}];

a = Join[{{1}}, Table[CoefficientList[Det[M[n]], x], {n, 1, 10}]];

Flatten[%] (End)

(PARI) T(n, k)=(1-n+k)*if(k<0|k>n, 0, n!/k!/(n-k)!)

Absolute values of columns 1, 2: A005563, A005564.

Sequence in context: A112168 A072516 A106450 this_sequence A143325 A128888 A163575

Adjacent sequences: A055134 A055135 A055136 this_sequence A055138 A055139 A055140

sign,tabl

Christian G. Bower (bowerc(AT)usa.net), Apr 25 2000

Additional comments from Michael Somos, Jul 04 2002