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Search: id:A091741
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| A091741 |
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Coefficients of certain polynomials related to array A078740 ((3,2)-Stirling2). |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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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.
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LINKS
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W. Lang, First 8 rows.
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FORMULA
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P(k, n) := ((-1)^k)*(k-1)!*(k-2)!*sum(((-1)^j)*binomial(k, j)*risefac(j-1, n)*risefac(j, n), j=2..k)/((n!^2)*(n+1)*product(n-p, p=1..ceiling(k/2)-1)) 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.
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CROSSREFS
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Sequence in context: A059844 A144284 A144285 this_sequence A061036 A144267 A011801
Adjacent sequences: A091738 A091739 A091740 this_sequence A091742 A091743 A091744
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KEYWORD
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sign,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 13 2004
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