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A091741
Coefficients of certain polynomials related to array A078740 ((3,2)-Stirling2).
1
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
2,2
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.
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.
CROSSREFS
Sequence in context: A144284 A144285 A292442 * A061036 A217020 A329066
KEYWORD
sign,easy,tabf
AUTHOR
Wolfdieter Lang, Feb 13 2004
STATUS
approved