

A093447


Triangle a(n,k) read by rows n which contain columns k=1,2,..,n, where each entry is the product of numbers (k1)*nT(k2)+1 through k*nT(k1).


2



1, 2, 3, 6, 20, 6, 24, 210, 72, 10, 120, 3024, 1320, 182, 15, 720, 55440, 32760, 4896, 380, 21, 5040, 1235520, 1028160, 175560, 13800, 702, 28, 40320, 32432400, 39070080, 7893600, 657720, 32736, 1190, 36, 362880, 980179200, 1744364160
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OFFSET

1,2


COMMENTS

This is built by starting from the sequence 1,2,....,T(n) in row n, where T(n) is the triangular number A000217(n) and packaging its first n, the next n1, the next n2,... up to the last number in groups and writing down the product of each group in one cell of the triangle. The first column is A000142. The second column is essentially A006963. The 3rd column is essentially A001763. The diagonal is A000217.  R. J. Mathar, Jul 26 2007


LINKS

Table of n, a(n) for n=1..39.


FORMULA

a(n,k)= [k*nT(k1)]!/[(k1)*nT(k2)]! where T(n)=A000217(n).  R. J. Mathar, Jul 26 2007


EXAMPLE

In factorized notation the triangle starts
1;
1*2, 3;
1*2*3, 4*5, 6;
1*2*3*4, 5*6*7, 8*9, 10;
1*2*3*4*5, 6*7*8*9, 10*11*12, 13*14, 15;
which gives
1;
2, 3;
6, 20, 6;
24, 210, 72, 10;
120, 3024, 1320, 182, 15;
720,55440,32760, 4896, 380, 21;


MAPLE

A000217 := proc(n) n*(n+1)/2 ; end: A093447 := proc(n, k) factorial(k*nA000217(k1))/factorial((k1)*nA000217(k2)) ; end: for n from 1 to 16 do for k from 1 to n do printf("%d, ", A093447(n, k)) ; od ; od: # R. J. Mathar, Jul 26 2007


CROSSREFS

Cf. A093445, A093446, A093448.
Sequence in context: A326030 A124066 A319204 * A321203 A259456 A334724
Adjacent sequences: A093444 A093445 A093446 * A093448 A093449 A093450


KEYWORD

nonn,tabl


AUTHOR

Amarnath Murthy, Apr 02 2004


EXTENSIONS

More terms from R. J. Mathar, Jul 26 2007


STATUS

approved



