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, 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.

Links

Table of n, a(n) for n=0..35.

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

Cf. A173018, A244028, A067804.

Sequence in context: A206489 A124399 A119600 * A219796 A222426 A107053

Adjacent sequences: A244024 A244025 A244026 * A244028 A244029 A244030

Keyword

nonn,tabl

Author

N. J. A. Sloane, based on email from Roger L. Bagula, Jun 21 2014

Status

approved