A092371 Triangle read by rows: T(n, k) = binomial(n, k) * binomial(n+k, n-k).

1, 6, 1, 18, 15, 1, 40, 90, 28, 1, 75, 350, 280, 45, 1, 126, 1050, 1680, 675, 66, 1, 196, 2646, 7350, 5775, 1386, 91, 1, 288, 5880, 25872, 34650, 16016, 2548, 120, 1, 405, 11880, 77616, 162162, 126126, 38220, 4320, 153, 1, 550, 22275, 205920, 630630

Offset

1,2

Comments

Related to the coefficients of x^k y^k in the n-th power of x^2 + x*y + 2*x + y + 1. - F. Chapoton, Jan 04 2025

Links

Table of n, a(n) for n=1..49.

Formula

T(n, k) = [x^(n-k)] F(-n, -n-k; 1; x). - Paul Barry, Sep 04 2008

Example

Triangle starts:
  [1]   1;
  [2]   6,    1;
  [3]  18,   15,     1;
  [4]  40,   90,    28,     1;
  [5]  75,  350,   280,    45,     1;
  [6] 126, 1050,  1680,   675,    66,    1;
  [7] 196, 2646,  7350,  5775,  1386,   91,   1;
  [8] 288, 5880, 25872, 34650, 16016, 2548, 120, 1;

Maple

T := (n, k) -> binomial(n, k) * binomial(n+k, n-k):  # Peter Luschny, Jan 04 2025

Prog

(PARI) T(n, k) = binomial(n, k)*binomial(n+k, n-k)

Crossrefs

First column = A002411, second column = A001297, third column = A107418, fourth column = A105251, fifth column = A104673.

Main diagonal = 1, second diagonal = A000384.

Cf. A063007, A006480 (central terms), A082759 (row sums + 1).

Cf. A104684.

Sequence in context: A277068 A369904 A373573 * A187552 A157386 A157396

Adjacent sequences: A092368 A092369 A092370 * A092372 A092373 A092374

Keyword

nonn,tabl

Author

Benoit Cloitre, Mar 20 2004

Status

approved