OFFSET
0,8
COMMENTS
Triangle of coefficients of polynomials P(n; x) = Permanent(M), where M=[m(i,j)] is n X n matrix defined by m(i,j)=x if 0<=i-j<=1 else m(i,j)=1. - Vladeta Jovovic, Jan 23 2003
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198.
LINKS
T. D. Noe, Rows n = 0..100 of triangle, flattened
FORMULA
G.f.: Sum(n!*(x*y)^n/(1+x*(y-1))^(2*n+1),n=0..infinity). [Vladeta Jovovic, Dec 13 2009]
EXAMPLE
1; 1,0; 1,1,0; 1,3,1,1; 1,6,6,8,3; ...
MAPLE
V := proc(n) local k; add( binomial(2*n-k, k)*(n-k)!*(x-1)^k, k=0..n); end; W := proc(r, s) coeff( V(r), x, s ); end; a := (n, k)->W(n, n-k);
MATHEMATICA
max = 9; f[x_, y_] := Sum[n!*((x*y)^n/(1 + x*(y-1))^(2*n+1)), {n, 0, max}]; Flatten[ MapIndexed[ Take[#1, #2[[1]]] & , CoefficientList[ Series[f[x, y], {x, 0, max}, {y, 0, max}], {x, y}]]] (*Jean-François Alcover, Jun 29 2012, after Vladeta Jovovic *)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Dec 02 2000
STATUS
approved