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A244027
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.
1
1, 4, 4, 66, 16, 66, 2416, 264, 264, 2416, 156190, 9664, 4356, 9664, 156190, 15724248, 624760, 159456, 159456, 624760, 15724248, 2275172004, 62896992, 10308540, 5837056, 10308540, 62896992, 2275172004, 447538817472, 9100688016, 1037800368, 377355040, 377355040, 1037800368, 9100688016, 447538817472
OFFSET
0,2
COMMENTS
Suggested by analogy with A067804.
EXAMPLE
Triangle begins:
[1]
[4, 4]
[66, 16, 66]
[2416, 264, 264, 2416]
[156190, 9664, 4356, 9664, 156190]
[15724248, 624760, 159456, 159456, 624760, 15724248]
...
MAPLE
Eul := (n, k) -> combinat[eulerian1](n, k):
T:=(n, k)->Eul(2*k + 1, k)*Eul(2*n - 2*k + 1, n - k);
for n from 0 to 10 do
lprint([seq(T(n, k), k=0..n)]);
od; # N. J. A. Sloane, Jun 21 2014
MATHEMATICA
Eul[n_ /; n >= 0, 0] = 1; Eul[n_, k_] /; k < 0 || k > n = 0;
Eul[n_, k_] := Eul[n, k] = (n-k) Eul[n-1, k-1] + (k+1) Eul[n-1, k];
T[n_, k_] := Eul[2k + 1, k] Eul[2n - 2k + 1, n-k];
Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 17 2020 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, based on email from Roger L. Bagula, Jun 21 2014
STATUS
approved