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 A256268 Table of k-fold factorials, read by antidiagonals. 7
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 3, 1, 1, 1, 24, 15, 4, 1, 1, 1, 120, 105, 28, 5, 1, 1, 1, 720, 945, 280, 45, 6, 1, 1, 1, 5040, 10395, 3640, 585, 66, 7, 1, 1, 1, 40320, 135135, 58240, 9945, 1056, 91, 8, 1, 1, 1, 362880, 2027025, 1106560, 208845, 22176, 1729, 120, 9, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS A variant of A142589. LINKS G. C. Greubel, Antidiagonal rows n = 0..100, flattened EXAMPLE 1  1   1    1     1       1         1... A000012 1  1   2    6    24     120       720... A000142 1  1   3   15   105     945     10395... A001147 1  1   4   28   280    3640     58240... A007559 1  1   5   45   585    9945    208845... A007696 1  1   6   66  1056   22176    576576... A008548 1  1   7   91  1729   43225   1339975... A008542 1  1   8  120  2640   76560   2756160... A045754 1  1   9  153  3825  126225   5175225... A045755 1  1  10  190  5320  196840   9054640... A045756 1  1  11  231  7161  293601  14977651... A144773 MAPLE seq(seq( mul(j*k+1, j=0..n-k-1), k=0..n), n=0..12); # G. C. Greubel, Mar 04 2020 MATHEMATICA T[n_, k_]= Product[j*k+1, {j, 0, n-1}]; Table[T[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 04 2020 *) PROG (PARI) T(n, k) = prod(j=0, n-1, j*k+1); for(n=0, 12, for(k=0, n, print1(T(n-k, k), ", "))) \\ G. C. Greubel, Mar 04 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-1]]);   end if; return T; end function; [T(n-k, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 04 2020 (Sage) [[ product(j*k+1 for j in (0..n-k-1)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 04 2020 (GAP) Flat(List([0..12], n-> List([0..n], k-> Product([0..n-k-1], j-> j*k+1) ))); # G. C. Greubel, Mar 04 2020 CROSSREFS Cf. Columns : A000012, A000012, A000384, A011199, A011245. Cf. Diagonals : A092985, A076111, A158887. Cf. A048994, A132393. Cf. A000142 ("1-fold"), A001147 (2-fold), A007559 (3), A007696 (4), A008548 (5), A008542 (6), A045754 (7), A045755 (8), A045756 (9), A144773 (10) Sequence in context: A335432 A229557 A332700 * A213275 A069777 A225816 Adjacent sequences:  A256265 A256266 A256267 * A256269 A256270 A256271 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Jun 01 2015 STATUS approved

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Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)