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A136657 Unsigned member s=2 of a family of generalizations of the (signed) Lah triangle A008297. All numbers divided by 2. 6
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; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
REFERENCES
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.
LINKS
FORMULA
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.
EXAMPLE
[1];[3,2];[12,18,4];[60,150,72,8];[360,1320,1020,240,16];...
MATHEMATICA
fallfac[n_, k_] := Pochhammer[n - k + 1, k]; a[n_, k_] := Sum[(-1)^(k - r)*Binomial[k, r]*fallfac[-2*r, n], {r, 0, k}]/(2*k!); Table[(-1)^n*a[n, k], {n, 0, 9}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 09 2013 *)
CROSSREFS
Sequence in context: A114798 A167639 A113205 * A006774 A361865 A356857
KEYWORD
easy,tabl,nonn
AUTHOR
Wolfdieter Lang, Feb 22 2008
STATUS
approved

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Last modified March 1 13:16 EST 2024. Contains 370433 sequences. (Running on oeis4.)