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%I #12 Aug 28 2019 17:37:29
%S 1,3,2,12,18,4,60,150,72,8,360,1320,1020,240,16,2520,12600,13860,5160,
%T 720,32,20160,131040,191520,99960,21840,2016,64,181440,1481760,
%U 2751840,1882440,571200,81984,5376,128,1814400,18144000,41489280,35622720
%N Unsigned member s=2 of a family of generalizations of the (signed) Lah triangle A008297. All numbers divided by 2.
%C In order to obtain the Lah triangle for s=+1 the sign of the s parameter in the Charalambides reference has been switched.
%C For more information see entry A136656 and the Charalambides reference.
%D 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.
%H W. Lang, <a href="/A136657/a136657.txt">First ten rows and more</a>.
%F 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.
%e [1];[3,2];[12,18,4];[60,150,72,8];[360,1320,1020,240,16];...
%t 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 *)
%K easy,tabl,nonn
%O 0,2
%A _Wolfdieter Lang_, Feb 22 2008
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