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

%I A130493 #14 Nov 07 2024 20:37:09
%S A130493 1,2,2,6,6,6,24,24,24,24,120,120,120,120,120,720,720,720,720,720,720,
%T A130493 5040,5040,5040,5040,5040,5040,5040,40320,40320,40320,40320,40320,
%U A130493 40320,40320,40320,362880,362880,362880,362880,362880,362880,362880,362880,362880
%N A130493 Triangle read by rows in which row n contains n! repeated n times.
%C A130493 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 A130493 Triangle, n! repeated n times per row.
%e A130493 First few rows of the triangle:
%e A130493    1;
%e A130493    2,  2;
%e A130493    6,  6,  6;
%e A130493   24, 24, 24, 24;
%e A130493   ...
%t A130493 Flatten[Table[Table[n!,{n}],{n,10}]] (* _Harvey P. Dale_, Dec 24 2014 *)
%t A130493 Table[PadRight[{},n,n!],{n,10}]//Flatten (* _Harvey P. Dale_, Jul 04 2022 *)
%o A130493 (Python)
%o A130493 from math import isqrt
%o A130493 from sympy import factorial
%o A130493 def A130493(n): return factorial((m:=isqrt(k:=n<<1))+(k>m*(m+1))) # _Chai Wah Wu_, Nov 07 2024
%Y A130493 Cf. A001563, A130477, A130478.
%K A130493 nonn,tabl
%O A130493 1,2
%A A130493 _Gary W. Adamson_, May 31 2007
%E A130493 More terms from _Sean A. Irvine_, Jul 19 2022