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

1,2

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).

Links

Table of n, a(n) for n=1..45.

Formula

Triangle, n! repeated n times per row.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001563, A130477, A130478.

Sequence in context: A358624 A048594 A178801 * A354638 A267516 A163118

Adjacent sequences: A130490 A130491 A130492 * A130494 A130495 A130496

Keyword

nonn,tabl

Author

Gary W. Adamson, May 31 2007

Extensions

More terms from Sean A. Irvine, Jul 19 2022

Status

approved