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Triangle read by rows in which row n contains n! repeated n times.
4

%I #14 Nov 07 2024 20:37:09

%S 1,2,2,6,6,6,24,24,24,24,120,120,120,120,120,720,720,720,720,720,720,

%T 5040,5040,5040,5040,5040,5040,5040,40320,40320,40320,40320,40320,

%U 40320,40320,40320,362880,362880,362880,362880,362880,362880,362880,362880,362880

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

%C 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).

%F Triangle, n! repeated n times per row.

%e First few rows of the triangle:

%e 1;

%e 2, 2;

%e 6, 6, 6;

%e 24, 24, 24, 24;

%e ...

%t Flatten[Table[Table[n!,{n}],{n,10}]] (* _Harvey P. Dale_, Dec 24 2014 *)

%t Table[PadRight[{},n,n!],{n,10}]//Flatten (* _Harvey P. Dale_, Jul 04 2022 *)

%o (Python)

%o from math import isqrt

%o from sympy import factorial

%o def A130493(n): return factorial((m:=isqrt(k:=n<<1))+(k>m*(m+1))) # _Chai Wah Wu_, Nov 07 2024

%Y Cf. A001563, A130477, A130478.

%K nonn,tabl,changed

%O 1,2

%A _Gary W. Adamson_, May 31 2007

%E More terms from _Sean A. Irvine_, Jul 19 2022