A123146 Triangle T(n, k) = (binomial(n,2))! / (k! * abs(k+1 - binomial(n,2))!), read by rows.

1, 1, 1, 3, 6, 3, 6, 30, 60, 60, 10, 90, 360, 840, 1260, 15, 210, 1365, 5460, 15015, 30030, 21, 420, 3990, 23940, 101745, 325584, 813960, 28, 756, 9828, 81900, 491400, 2260440, 8288280, 24864840, 36, 1260, 21420, 235620, 1884960, 11686752, 58433760, 242082720, 847289520

Offset

0,4

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n, k) = (binomial(n+1,2))! / (k! * abs(k+1 - binomial(n+1,2))!).

Example

Triangle begins as:
   1;
   1,   1;
   3,   6,    3;
   6,  30,   60,    60;
  10,  90,  360,   840,   1260;
  15, 210, 1365,  5460,  15015,   30030;
  21, 420, 3990, 23940, 101745,  325584,  813960;
  28, 756, 9828, 81900, 491400, 2260440, 8288280, 24864840;

Mathematica

T[n_, k_]:= (n*(n+1)/2)!/(k!*(Abs[k+1 -(n*(n+1)/2)])!);
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(Magma) [Factorial(Binomial(n+1, 2))/(Factorial(k)*Factorial(Abs(k+1 - Binomial(n+1, 2)))): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 16 2023
(SageMath)
def A123146(n, k): return factorial(binomial(n+1, 2))/(factorial(k)*factorial(abs(k+1 - binomial(n+1, 2))))
flatten([[A123146(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Jul 16 2023

Crossrefs

Sequence in context: A323503 A303129 A170859 * A016661 A201143 A326935

Adjacent sequences: A123143 A123144 A123145 * A123147 A123148 A123149

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Oct 01 2006

Extensions

Edited by G. C. Greubel, Jul 16 2023

Status

approved