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 A245334 A factorial-like triangle read by rows: T(0,0) = 1; T(n+1,0) = T(n,0)+1; T(n+1,k+1) = T(n,0)*T(n,k), k=0..n. 25
 1, 2, 1, 3, 4, 2, 4, 9, 12, 6, 5, 16, 36, 48, 24, 6, 25, 80, 180, 240, 120, 7, 36, 150, 480, 1080, 1440, 720, 8, 49, 252, 1050, 3360, 7560, 10080, 5040, 9, 64, 392, 2016, 8400, 26880, 60480, 80640, 40320, 10, 81, 576, 3528, 18144, 75600, 241920, 544320 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS row(0) = {1}; row(n+1) = row(n) multiplied by n and prepended with (n+1); A111063(n+1) = sum of n-th row; T(2*n,n) = A002690(n), central terms; T(n,0) = n + 1; T(n,1) = A000290(n), n > 0; T(n,2) = A011379(n-1), n > 1; T(n,3) = A047927(n), n > 2; T(n,4) = A192849(n-1), n > 3; T(n,5) = A000142(5) * A027810(n-5), n > 4; T(n,6) = A000142(6) * A027818(n-6), n > 5; T(n,7) = A000142(7) * A056001(n-7), n > 6; T(n,8) = A000142(8) * A056003(n-8), n > 7; T(n,9) = A000142(9) * A056114(n-9), n > 8; T(n,n-10) = 11 * A051431(n-10), n > 9; T(n,n-9) = 10 * A049398(n-9), n > 8; T(n,n-8) = 9 * A049389(n-8), n > 7; T(n,n-7) = 8 * A049388(n-7), n > 6; T(n,n-6) = 7 * A001730(n), n > 5; T(n,n-5) = 6 * A001725(n), n > 5; T(n,n-4) = 5 * A001720(n), n > 4; T(n,n-3) = 4 * A001715(n), n > 2; T(n,n-2) = A070960(n), n > 1; T(n,n-1) = A052849(n), n > 0; T(n,n) = A000142(n); T(n,k) = A137948(n,k) * A007318(n,k), 0 <= k <= n. LINKS Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened FORMULA T(n,k) = n!*(n+1-k)/(n-k)!. - Werner Schulte, Sep 09 2017 EXAMPLE .  0:   1; .  1:   2,  1; .  2:   3,  4,   2; .  3:   4,  9,  12,    6; .  4:   5, 16,  36,   48,    24; .  5:   6, 25,  80,  180,   240,   120; .  6:   7, 36, 150,  480,  1080,  1440,    720; .  7:   8, 49, 252, 1050,  3360,  7560,  10080,   5040; .  8:   9, 64, 392, 2016,  8400, 26880,  60480,  80640,  40320; .  9:  10, 81, 576, 3528, 18144, 75600, 241920, 544320, 725760, 362880. MATHEMATICA Table[(n!)/((n - k)!)*(n + 1 - k), {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Sep 10 2017 *) PROG (Haskell) a245334 n k = a245334_tabl !! n !! k a245334_row n = a245334_tabl !! n a245334_tabl = iterate (\row@(h:_) -> (h + 1) : map (* h) row) [1] CROSSREFS Cf. A111063 (row sums), A240993 (row products), A002690 (central terms). Cf. A000290, A011379, A027810, A027818, A047927, A056001, A056003, A056114, A192849. Cf. A000142, A001715, A001720, A001725, A001730, A049388, A049389, A049398, A051431, A052849, A070960. Cf. A007318, A137948. Sequence in context: A128544 A120058 A208532 * A102756 A086614 A108959 Adjacent sequences:  A245331 A245332 A245333 * A245335 A245336 A245337 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Aug 30 2014 STATUS approved

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Last modified April 21 08:49 EDT 2021. Contains 343148 sequences. (Running on oeis4.)