A271704 - OEIS

%I #6 Apr 20 2016 05:35:14

%S 1,0,1,0,3,1,0,11,8,1,0,49,57,15,1,0,261,424,174,24,1,0,1631,3425,

%T 1930,410,35,1,0,11743,30336,21855,6320,825,48,1,0,95901,294553,

%U 259161,95235,16835,1491,63,1,0,876809,3123632,3251500,1452976,325150,38864,2492,80,1

%N Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*L(j,k), L the unsigned Lah numbers A271703, for n>=0 and 0<=k<=n.

%e Triangle starts:

%e [1]

%e [0, 1]

%e [0, 3,     1]

%e [0, 11,    8,     1]

%e [0, 49,    57,    15,    1]

%e [0, 261,   424,   174,   24,   1]

%e [0, 1631,  3425,  1930,  410,  35,  1]

%e [0, 11743, 30336, 21855, 6320, 825, 48, 1]

%p L := (n,k) -> `if`(k<0 or k>n,0,(n-k)!*binomial(n,n-k)*binomial(n-1,n-k)):

%p T := (n,k) -> add(L(j,k)*binomial(-j,-n)*(-1)^(n-j), j=0..n):

%p seq(seq(T(n,k), k=0..n), n=0..9);

%Y A001339 (col. 1), A005563 (diag. n,n-1).

%Y Cf. A271703.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Apr 14 2016