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

0,2

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

Table of n, a(n) for n=0..39.

W. Lang, First ten rows and more.

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

Adjacent sequences: A136654 A136655 A136656 * A136658 A136659 A136660

Keyword

easy,tabl,nonn

Author

Wolfdieter Lang, Feb 22 2008

Status

approved