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A089278
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Coefficient triangle for computation of column numbers of triangle A071951 (Legendre-Stirling).
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9
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1, -1, 3, 1, -15, 24, -7, 405, -2268, 2500, 2, -405, 6048, -20000, 16875, -11, 7425, -266112, 2000000, -4640625, 3176523, 143, -312741, 25474176, -390000000, 1879453125, -3344878719, 1927561216, -143, 995085, -178319232, 5250000000, -46986328125, 163899057231, -236126248960
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The k-th column sequence A071951(n+k,k), n>=0, is sum(a(k,p)*(p*(p+1))^n,p=1..k)/A089500(k), k>=1.
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LINKS
| W. Lang, First 7 rows.
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FORMULA
| a(n, m)= A089500(n)*(((-1)^(m+n))*(2*m+1)*((m*(m+1))^n)/((m+n+1)!*(n-m)!)).
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EXAMPLE
| [1]; [ -1,3]; [1,-15,24]; [ -7,405,-2268,2500]; ...
Sequence A071951(n+3,3)= A016309(n)= [1,20,292,...] has a(n)=
(1*(1*2)^n - 15*(2*3)^n + 24*(3*4)^n)/10.
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CROSSREFS
| Sequence in context: A178657 A156289 A095922 * A087071 A053485 A160628
Adjacent sequences: A089275 A089276 A089277 * A089279 A089280 A089281
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KEYWORD
| sign,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Nov 07 2003
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