A259097 Triangle read by rows: T(n,r) = binomial(n,r)*binomial(2*n-3*r-4,n-2*r-2)/(n-r-1), n >= 2, r = 0..floor(n/2)-1.

1, 1, 2, 2, 5, 5, 14, 15, 5, 42, 49, 21, 132, 168, 84, 14, 429, 594, 336, 84, 1430, 2145, 1350, 420, 42, 4862, 7865, 5445, 1980, 330, 16796, 29172, 22022, 9075, 1980, 132, 58786, 109174, 89232, 40898, 10725, 1287, 208012, 411502, 361998, 182182, 55055, 9009, 429, 742900, 1560090, 1469650, 804440, 273273, 55055, 5005

Offset: 2

Author

N. J. A. Sloane, Jun 22 2015

Keywords

• nonn
• tabf

Examples

			Triangle begins:
        1;
        1;
        2,       2;
        5,       5;
       14,      15,       5;
       42,      49,      21;
      132,     168,      84,      14;
      429,     594,     336,      84;
     1430,    2145,    1350,     420,      42;
     4862,    7865,    5445,    1980,     330;
    16796,   29172,   22022,    9075,    1980,    132;
    58786,  109174,   89232,   40898,   10725,   1287;
   208012,  411502,  361998,  182182,   55055,   9009,   429;
   742900, 1560090, 1469650,  804440,  273273,  55055,  5005;
  2674440, 5943200, 5969040, 3527160, 1324960, 312312, 40040, 1430;
  ...
		

Links

• Indranil Ghosh, Rows 2..125, flattened
• F. R. Bernhart & N. J. A. Sloane, Emails, April-May 1994

Crossrefs

Row sums are A006343. Right-hand boundary is a mixture of A000108 and A002054.

Programs

Magma

/* As triangle: */ [[Binomial(n,k)*Binomial(2*n-3*k-4,n-2*k-2)/(n-k-1): k in [0..Floor(n/2)-1]]: n in [2..15]]; // Vincenzo Librandi, Jun 22 2015

Maple

T:=(n,r) -> binomial(n,r)*binomial(2*n-3*r-4,n-2*r-2)/(n-r-1);
v:=n->[seq(T(n,r),r=0..floor(n/2)-1)];
for n from 2 to 16 do lprint(v(n)); od:

Mathematica

Flatten[Table[Binomial[n,r] Binomial[2n-3r-4,n-2r-2]/(n-r-1),{n,2,16},{r,0,Floor[(n/2)]-1}]] (* Indranil Ghosh, Feb 20 2017 *)