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A058057 Triangle giving coefficients of ménage hit polynomials. 8
1, 1, 0, 1, 1, 0, 1, 3, 1, 1, 1, 6, 6, 8, 3, 1, 10, 20, 38, 35, 16, 1, 15, 50, 134, 213, 211, 96, 1, 21, 105, 385, 915, 1479, 1459, 675, 1, 28, 196, 952, 3130, 7324, 11692, 11584, 5413, 1, 36, 336, 2100, 9090, 28764, 65784, 104364, 103605, 48800 (list; table; graph; refs; listen; history; text; internal format)
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

Diagonals give A000271, A000426, A000222, A000386, A000450, A058085, A058086.

Cf. A080018, A080061.

Sequence in context: A291722 A297672 A256973 * A124372 A126470 A179701

Adjacent sequences:  A058054 A058055 A058056 * A058058 A058059 A058060

KEYWORD

nonn,easy,nice,tabl

AUTHOR

N. J. A. Sloane, Dec 02 2000

STATUS

approved

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Last modified August 19 07:13 EDT 2022. Contains 356216 sequences. (Running on oeis4.)