0,5

Note: rows continue as factorials - stopped at second factorial for clarity.

T(n,n)=T(n,n+1)=n!. Sum of row n = n! + s(n,2), where s(n,2) are signless Sirling numbers of the first kind (A081046). T(n,k)=A109822(n,k) for 1<=k<=n (i.e. triangle without the last column is A109822). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 03 2005

R. P. Stanley, Ordering events in Minkowski space

T(n+1, i)=n*T(n, i-1)+T(n, i)

T(n, k)=sum(|stirling1(n, n-i)|, i=0..k-1) for 1<=k<=n. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 03 2005

Triangle begins:

*0.........................1

*1......................1.....1

*2...................1.....2.....2

*3................1.....4.....6.....6

*4.............1.....7....18....24....24

*5..........1....11....46....96...120...120

*6.......1....16...101...326...600...720...720

*7....1....22...197...932..2556..4320..5040..5040

T(5,3)=46 because 4*7+18=46

T:=proc(n, k) if k=1 then 1 elif k=n+1 then n! else T(n-1, k)+(n-1)*T(n-1, k-1) fi end: for n from 0 to 11 do seq(T(n, k), k=1..n+1) od; # yields sequence in triangular form with(combinat): T:=(n, k)->sum(abs(stirling1(n, n-i)), i=0..k-1): for n from 0 to 11 do seq(T(n, k), k=1..n+1) od; # yields sequence in triangular form (Deutsch)

Cf. A081046, A109822.

Sequence in context: A061598 A071946 A053495 this_sequence A167622 A084606 A137399

Adjacent sequences: A096744 A096745 A096746 this_sequence A096748 A096749 A096750

nonn,easy,tabl

Thomas J Engelsma (tom(AT)opertech.com), Dec 05 2004

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 03 2005