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 A142589 Square array T(n,m) = Product_{i=0..m} (1+n*i) read by antidiagonals. 4
 1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 24, 15, 4, 1, 1, 120, 105, 28, 5, 1, 1, 720, 945, 280, 45, 6, 1, 1, 5040, 10395, 3640, 585, 66, 7, 1, 1, 40320, 135135, 58240, 9945, 1056, 91, 8, 1, 1, 362880, 2027025, 1106560, 208845, 22176, 1729, 120, 9, 1, 1, 3628800, 34459425, 24344320, 5221125, 576576, 43225, 2640, 153, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Antidiagonal sums are {1, 2, 4, 11, 45, 260, 1998, 19735, 244797, 3729346, 68276276, ...}. LINKS G. C. Greubel, Antidiagonal rows n = 0..100, flattened EXAMPLE The transpose of the array is:     1,    1,     1,     1,      1,      1,      1,      1,     1,     1,    2,     3,     4,      5,      6,      7,      8,     9,     1,    6,    15,    28,     45,     66,     91,     120,   153, ... A000384     1,   24,   105,   280,    585,   1056,   1729,    2640,  3825, ... A011199     1,  120,   945,  3640,   9945,  22176,  43225,   76560, 126225,... A011245     1,  720, 10395, 58240, 208845, 576576, 1339975, 2756160,...         /      |       \       \ MAPLE T:= (n, k)-> `if`(n=0, 1, mul(j*k+1, j=0..n)): seq(seq(T(n-k, k), k=0..n), n=0..12); # G. C. Greubel, Mar 05 2020 MATHEMATICA T[n_, k_]= If[n==0, 1, Product[1 + k*i, {i, 0, n}]]; Table[T[n-k, k], {n, 0, 10}, {k, 0, n}]//Flatten PROG (PARI) T(n, k) = if(n==0, 1, prod(j=0, n, j*k+1) ); for(n=0, 12, for(k=0, n, print1(T(n-k, k), ", "))) \\ G. C. Greubel, Mar 05 2020 (MAGMA) function T(n, k)   if k eq 0 or n eq 0 then return 1;   else return (&*[j*k+1: j in [0..n]]);   end if; return T; end function; [T(n-k, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 05 2020 (Sage) def T(n, k):     if (k==0 and n==0): return 1     else: return product(j*k+1 for j in (0..n)) [[T(n-k, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 05 2020 CROSSREFS Cf. A000142, A006882(2n-1) = A001147, A007661(3n-2) = A007559, A007662(4n-3) = A007696, A153274. Sequence in context: A181644 A144351 A213936 * A284308 A172400 A226691 Adjacent sequences:  A142586 A142587 A142588 * A142590 A142591 A142592 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 22 2008 EXTENSIONS Edited by M. F. Hasler, Oct 28 2014 More terms added by G. C. Greubel, Mar 05 2020 STATUS approved

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Last modified April 5 10:33 EDT 2020. Contains 333239 sequences. (Running on oeis4.)