A136657 Unsigned member s=2 of a family of generalizations of the (signed) Lah triangle A008297. All numbers divided by 2.

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

Offset: 0

Author

Wolfdieter Lang, Feb 22 2008

Keywords

• easy
• tabl
• nonn

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.

Examples

			[1];[3,2];[12,18,4];[60,150,72,8];[360,1320,1020,240,16];...
		

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

• W. Lang, First ten rows and more.

Programs

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 *)

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.