A379100 Triangle read by rows: T(n, k) = binomial(2*k, k) * binomial(2*n, n) / (n + 1).

1, 1, 2, 2, 4, 12, 5, 10, 30, 100, 14, 28, 84, 280, 980, 42, 84, 252, 840, 2940, 10584, 132, 264, 792, 2640, 9240, 33264, 121968, 429, 858, 2574, 8580, 30030, 108108, 396396, 1472328, 1430, 2860, 8580, 28600, 100100, 360360, 1321320, 4907760, 18404100

Offset

0,3

Links

Table of n, a(n) for n=0..44.

Formula

T(n, k) = ((2*k)! * (2*n)!) / ((k! * n!)^2 * (n+1)).

Example

  [0]   1;
  [1]   1,   2;
  [2]   2,   4,   12;
  [3]   5,  10,   30,  100;
  [4]  14,  28,   84,  280,   980;
  [5]  42,  84,  252,  840,  2940,  10584;
  [6] 132, 264,  792, 2640,  9240,  33264, 121968;
  [7] 429, 858, 2574, 8580, 30030, 108108, 396396, 1472328;

Maple

T := (n, k) -> binomial(2*k, k) * binomial(2*n, n) / (n + 1):
seq(seq(T(n, k), k = 0..n), n = 0..8);

Crossrefs

Cf. A002894, A000888, A270577, A379099 (row sums).

Sequence in context: A202795 A256890 A110476 * A330762 A059343 A285944

Adjacent sequences: A379097 A379098 A379099 * A379101 A379102 A379103

Keyword

nonn,tabl

Author

Peter Luschny, Dec 15 2024

Status

approved