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Search: id:A136657
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| A136657 |
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Unsigned member s=2 of a family of generalizations of the (signed) Lah triangle A008297. All numbers divided by 2. |
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+0
6
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| 1, 3, 2, 12, 18, 4, 60, 150, 72, 8, 360, 1320, 1020, 240, 16, 2520, 12600, 13860, 5160, 720, 32, 20160, 131040, 191520, 99960, 21840, 2016, 64, 181440, 1481760, 2751840, 1882440, 571200, 81984, 5376, 128, 1814400, 18144000, 41489280, 35622720
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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In order to obtain the Lah triangle for s=+1 the sign of the s parameter in the Charalambides reference has been switched.
For more information see entry A136656 and the Charalambides reference.
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REFERENCES
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Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, ch. 8.4 p. 301 ff, with s -> -s. Table 8.3 for s=-2 and multiplied by(-1)^n, divided by 2.
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LINKS
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W. Lang, First ten rows and more.
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FORMULA
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a(n,k)=sum(((-1)^(k-r))*binomial(k,r)*fallfac(-2*r,n),r=0..k)/(2*k!), n>=k>=1. From the Charalambides reference Theorem 8.15, p. 306 for s=-2, divided by 2.
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EXAMPLE
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[1];[3,2];[12,18,4];[60,150,72,8];[360,1320,1020,240,16];...
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CROSSREFS
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Adjacent sequences: A136654 A136655 A136656 this_sequence A136658 A136659 A136660
Sequence in context: A152550 A114798 A113205 this_sequence A006774 A086551 A007214
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KEYWORD
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easy,tabl,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Feb 22 2008
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