A059374 Triangle read by rows, T(n, k) = Sum_{i=0..n} L'(n, n-i) * binomial(i, k), for k = 0..n-1.

1, 3, 2, 13, 18, 6, 73, 156, 108, 24, 501, 1460, 1560, 720, 120, 4051, 15030, 21900, 15600, 5400, 720, 37633, 170142, 315630, 306600, 163800, 45360, 5040, 394353, 2107448, 4763976, 5891760, 4292400, 1834560, 423360, 40320

Offset: 1

Author

Vladeta Jovovic, Jan 28 2001

Keywords

• easy
• nonn
• tabl

Comments

L'(n, i) are unsigned Lah numbers (Cf. A008297).

Examples

			Triangle begins:
  [1],
  [3, 2],
  [13, 18, 6],
  [73, 156, 108, 24],
  [501, 1460, 1560, 720, 120],
  ...
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. T(n, 0) = A000262, A025168 (row sums), A000012 (alternating row sums), A059110.

Cf. A008297, A271703.

Programs

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 *)

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

Formula

E.g.f.: exp(x/(1-(1+y)*x))/(1-(1+y)*x)^2. - Vladeta Jovovic, May 10 2003