A059446 Triangle T(n,k) = coefficient of x^n*y^k/(n!*k!) in 1/(1-x-y-x*y), read by rows in order 00, 10, 01, 20, 11, 02, ...

1, 1, 1, 2, 3, 2, 6, 10, 10, 6, 24, 42, 52, 42, 24, 120, 216, 300, 300, 216, 120, 720, 1320, 1968, 2268, 1968, 1320, 720, 5040, 9360, 14640, 18576, 18576, 14640, 9360, 5040, 40320, 75600, 122400, 166320, 184896, 166320, 122400, 75600, 40320

Offset: 0

Author

N. J. A. Sloane, Feb 02 2001

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
  1;
  1,1;
  2,3,2;
  6,10,10,6;
  ...
		

Crossrefs

Cf. A008288.

Programs

Maple

read transforms; SERIES2(1/(1-x-y-x*y),x,y,12): SERIES2TOLISTMULT(%,x,y,12);

Mathematica

T[n_, k_] := n!*2^k*Hypergeometric2F1[-k, -k, -n, 1/2]; Table[T[n,k], {n, 0, 8}, {k, 0, n}]//Flatten (* Detlef Meya, Aug 18 2024 *)

Formula

E.g.f.: 1/(1-x-y-x*y).

T(n, k) = n!*2^k*Hypergeometric2F1([-k, -k], [-n], 1/2). - Detlef Meya, Aug 18 2024