A153273 Triangle read by rows: T(n,k) = Product_{i=0..k-2} (i*n + n - 1).

1, 2, 10, 3, 21, 231, 4, 36, 504, 9576, 5, 55, 935, 21505, 623645, 6, 78, 1560, 42120, 1432080, 58715280, 7, 105, 2415, 74865, 2919735, 137227545, 7547514975, 8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640, 9, 171, 4959, 193401, 9476649, 559122291, 38579438079, 3047775608241, 271252029133449

Offset: 2

Author

Roger L. Bagula, Dec 22 2008

Keywords

• nonn
• tabl
• easy

Comments

Row sums are {1, 12, 255, 10120, 646145, 60191124, 7687739647, 1288641721680, 274338952977249, 72299818200530140, ...}.

A153187 without its diagonal. - R. J. Mathar, Sep 04 2016

Examples

			Triangle begins as:
  1;
  2,  10;
  3,  21,  231;
  4,  36,  504,   9576;
  5,  55,  935,  21505,  623645;
  6,  78, 1560,  42120, 1432080,  58715280;
  7, 105, 2415,  74865, 2919735, 137227545,  7547514975;
  8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640;
		

Links

• G. C. Greubel, Rows n = 2..100 of triangle, flattened

Crossrefs

Cf. A000027, A014105, A033594.

Programs

GAP

Flat(List([2..12], n-> List([2..n], k-> Product([0..k-2], j-> (j+1)*n-1) ))); # G. C. Greubel, Mar 05 2020

Magma

[(&*[j*n+n-1: j in [0..k-2]]): k in [2..n], n in [2..12]]; // G. C. Greubel, Mar 05 2020

Maple

A153273 := proc(n,m)
    local i;
    mul( n-1+i*n, i=0..m-2) ;
end proc:
seq(seq( A153273(n,m), m=2..n), n=2..12) ; # R. J. Mathar, Sep 04 2016

Mathematica

Table[n^(k-1)*Pochhammer[(n-1)/n, k-1], {n,2,12}, {k,2,n}]//Flatten (* modified by G. C. Greubel, Mar 05 2020 *)

PARI

T(n,k) = prod(j=0, k-2, j*n+n-1);
for(n=2,12, for(k=2,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Mar 05 2020

Sage

[[n^(k-1)*rising_factorial((n-1)/n, k-1) for k in (2..n)] for n in (2..12)] # G. C. Greubel, Mar 05 2020

Extensions

Edited by G. C. Greubel, Mar 05 2020