OFFSET
1,2
COMMENTS
L'(n, i) are unsigned Lah numbers (Cf. A008297).
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
E.g.f.: exp(x/(1-(1+y)*x))/(1-(1+y)*x)^2. - Vladeta Jovovic, May 10 2003
EXAMPLE
Triangle begins:
[1],
[3, 2],
[13, 18, 6],
[73, 156, 108, 24],
[501, 1460, 1560, 720, 120],
...
MATHEMATICA
t[n_, k_] := Sum[ Binomial[n-1, n-i-1]*n!/(n-i)!*Binomial[i, k], {i, 0, n}]; Table[t[n, k], {n, 1, 8}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Mar 22 2013 *)
PROG
(PARI) for(n=1, 10, for(k=0, n-1, print1(sum(j=0, n, binomial(j, k)* binomial(n-1, n-j-1)*n!/(n-j)!), ", "))) \\ G. C. Greubel, Jan 29 2018
CROSSREFS
KEYWORD
AUTHOR
Vladeta Jovovic, Jan 28 2001
STATUS
approved