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 A093447 Triangle a(n,k) read by rows n which contain columns k=1,2,..,n, where each entry is the product of numbers (k-1)*n-T(k-2)+1 through k*n-T(k-1). 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 (list; table; graph; refs; listen; history; text; internal format)
 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 n-1, the next n-2,... 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 FORMULA a(n,k)= [k*n-T(k-1)]!/[(k-1)*n-T(k-2)]! 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*n-A000217(k-1))/factorial((k-1)*n-A000217(k-2)) ; 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

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)