A123147 Triangle T(n, k) = (n+2)!*(n*(n+1)*(2*n+1)/6)!/( (k^2)! * abs(2 + 2*k^2 - (n*(n + 1)*(2*n+1)/6))! ), read by rows.

1, 6, 1, 480, 2880, 1, 21840, 2882880, 18162144000, 40040, 626400, 473558400, 3270820512960000, 145032891526185062400000, 380331009246988800000, 14968800, 41254012800, 22288874800832640000, 17065364402126896882035609600000, 59861520269419187714435515882890362880000000, 687565882176828511388211047069939545826918400000000

Offset

0,2

Links

G. C. Greubel, Rows n = 0..15 of the triangle, flattened

Formula

T(n, k) = (n+2)!*(n*(n+1)*(2*n+1)/6)!/( (k^2)! * abs(2 + 2*k^2 - (n*(n + 1)*(2*n+1)/6))! ).

Example

Triangle begins as:
      1;
      6,       1;
    480,    2880,           1;
  21840, 2882880, 18162144000, 40040;

Mathematica

T[n_, k_]= (n+2)!*(n*(n+1)*(2*n+1)/6)!/((k^2)!*Abs[2 +2*k^2 -(n*(n + 1)*(2*n+1)/6)]!);
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(Magma)
F:=Factorial;
A123147:= func< n, k | F(n+2)*F(Floor(n*(n+1)*(2*n+1)/6))/( F(k^2) * F(Abs(Floor(2 + 2*k^2 - n*(n+1)*(2*n+1)/6))) ) >;
[A123147(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Jul 16 2023
(SageMath)
f=factorial
def A123147(n, k): return f(n+2)*f(n*(n+1)*(2*n+1)/6)/(f(k^2)*f(abs(2 + 2*k^2 - (n*(n+1)*(2*n+1)/6))) )
flatten([[A123147(n, k) for k in range(n+1)] for n in range(11)]) # G. C. Greubel, Jul 16 2023

Crossrefs

Cf. A123146.

Sequence in context: A352012 A183284 A224476 * A119831 A369016 A224842

Adjacent sequences: A123144 A123145 A123146 * A123148 A123149 A123150

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Oct 01 2006

Extensions

Edited by G. C. Greubel, Jul 16 2023

Status

approved