OFFSET
0,5
LINKS
P. Di Francesco, P. Zinn-Justin and J.-B. Zuber, Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops, arXiv:math-ph/0410002, 2004.
W. F. Lunnon, The Pascal matrix, Fib. Quart. vol. 15 (1977) pp. 201-204.
Luca Guido Molinari, Graphene nanocones and Pascal matrices, arXiv:2206.14428 [math.CO], 2022.
EXAMPLE
1;
1,1;
1,3,1;
1,9,9,1;
1,29,72,29,1;
...
MATHEMATICA
P[n_] := Table[Binomial[i + j - 2, i - 1], {i, 1, n}, {j, 1, n}];
row[0] = {1};
row[n_] := CoefficientList[ CharacteristicPolynomial[P[n], x], x] // Abs;
Table[row[n], {n, 0, 9}] // Flatten (* Jean-François Alcover, Aug 09 2018 *)
PROG
(PARI) T(n, k)=if(n<0, 0, (-1)^(n+k)*polcoeff(charpoly(matrix(n, n, i, j, binomial(i+j-2, i-1))), k))
(PARI) T(n, k)=if(n<0, 0, polcoeff(charpoly(-matrix(n, n, i, j, binomial(i+j-2, i-1))), k))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Fred Lunnon, Dec 11 1999
STATUS
approved