A130493 Triangle read by rows in which row n contains n! repeated n times.

1, 2, 2, 6, 6, 6, 24, 24, 24, 24, 120, 120, 120, 120, 120, 720, 720, 720, 720, 720, 720, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880

Offset: 1

Author

Gary W. Adamson, May 31 2007

Keywords

• nonn
• tabl

Comments

Row sums = A001563: (1, 4, 18, 96, 600, 4320, ...). A130477(n,k) * A130478(n,k) = A130493(n,k). Example: take dot products of rows with equal numbers of terms in A130477 and A130478, (1, 3, 8, 12) dot (24, 8, 3, 2) = (24, 24, 24, 24).

Examples

			First few rows of the triangle:
   1;
   2,  2;
   6,  6,  6;
  24, 24, 24, 24;
  ...
		

Crossrefs

Cf. A001563, A130477, A130478.

Programs

Mathematica

Flatten[Table[Table[n!,{n}],{n,10}]] (* Harvey P. Dale, Dec 24 2014 *)
Table[PadRight[{},n,n!],{n,10}]//Flatten (* Harvey P. Dale, Jul 04 2022 *)

Python

from math import isqrt
from sympy import factorial
def A130493(n): return factorial((m:=isqrt(k:=n<<1))+(k>m*(m+1))) # Chai Wah Wu, Nov 07 2024

Formula

Triangle, n! repeated n times per row.

Extensions

More terms from Sean A. Irvine, Jul 19 2022