A244027 - OEIS

%I #15 Feb 17 2020 07:34:39

%S 1,4,4,66,16,66,2416,264,264,2416,156190,9664,4356,9664,156190,

%T 15724248,624760,159456,159456,624760,15724248,2275172004,62896992,

%U 10308540,5837056,10308540,62896992,2275172004,447538817472,9100688016,1037800368,377355040,377355040,1037800368,9100688016,447538817472

%N Triangle read by rows: T(n,k) = Eul(2*k + 1, k)*Eul(2*n - 2*k + 1, n - k) (0 <= k <= n), where Eul(i,j) are the Eulerian numbers A173018.

%C Suggested by analogy with A067804.

%e Triangle begins:

%e [1]

%e [4, 4]

%e [66, 16, 66]

%e [2416, 264, 264, 2416]

%e [156190, 9664, 4356, 9664, 156190]

%e [15724248, 624760, 159456, 159456, 624760, 15724248]

%e ...

%p Eul := (n, k) -> combinat[eulerian1](n, k):

%p T:=(n,k)->Eul(2*k + 1, k)*Eul(2*n - 2*k + 1, n - k);

%p for n from 0 to 10 do

%p lprint([seq(T(n,k),k=0..n)]);

%p od; # _N. J. A. Sloane_, Jun 21 2014

%t Eul[n_ /; n >= 0, 0] = 1; Eul[n_, k_] /; k < 0 || k > n = 0;

%t Eul[n_, k_] := Eul[n, k] = (n-k) Eul[n-1, k-1] + (k+1) Eul[n-1, k];

%t T[n_, k_] := Eul[2k + 1, k] Eul[2n - 2k + 1, n-k];

%t Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Feb 17 2020 *)

%Y Cf. A173018, A244028, A067804.

%K nonn,tabl

%O 0,2

%A _N. J. A. Sloane_, based on email from _Roger L. Bagula_, Jun 21 2014