A091741 Coefficients of certain polynomials related to array A078740 ((3,2)-Stirling2).

1, 4, 1, -36, 8, 9, 1, -288, 18, 83, 18, 1, 7200, -2352, -2366, 165, 205, 27, 1, 86400, -18000, -31936, -926, 2735, 565, 41, 1, -4233600, 1647360, 1541304, -286084, -187614, -1491, 7056, 1014, 54, 1, -67737600, 19968480, 27275064, -2562556, -3442594, -254583, 115605, 24906

Offset: 2

Author

Wolfdieter Lang, Feb 13 2004

Keywords

• sign
• easy
• tabf

Comments

A078740(n,k)=(((-1)^k)/k!)*sum(((-1)^j)*binomial(k,j)*risefac(j-1,n)*risefac(j,n),j=2..k) with risefac(x,n) := Pochhammer(x,n).

The sequence of row lengths of this array is [1,2,4,5,7,8,10,11,...] = A001651(k-2) = floor((3*k-4)/2) for k>=2.

Links

• Wolfdieter Lang, First 8 rows.

Formula

P(k, n) := (-1)^k*(k-1)!*(k-2)!*(Sum_{j=2..k} (-1)^j*binomial(k, j)*risefac(j-1, n)*risefac(j, n))/(n!^2*(n+1)*Product_{p=1..ceiling(k/2)-1} (n-p)) is a polynomial in n of degree A032766(k-2), k >= 2. risefac(x, n) := Pochhammer(x, n).

a(k, m) = [n^m]P(k, n) with the above defined polynomials in n defined for k >= 2.