A156047 Triangle read by rows: T(n, k) = (n+1)!*(1/k + 1/(n-k+1)).

4, 9, 9, 32, 24, 32, 150, 100, 100, 150, 864, 540, 480, 540, 864, 5880, 3528, 2940, 2940, 3528, 5880, 46080, 26880, 21504, 20160, 21504, 26880, 46080, 408240, 233280, 181440, 163296, 163296, 181440, 233280, 408240, 4032000, 2268000, 1728000, 1512000, 1451520, 1512000, 1728000, 2268000, 4032000

Offset

1,1

Comments

Row sums are (n+1)*A052517(n+2) = {4, 18, 88, 500, 3288, 24696, 209088, 1972512, 20531520, ...}.

Links

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Formula

T(n, k) = (n+1)*(n+1)!/(k*(n-k+1)).

Sum_{k=1..n} T(n,k) = 2*(n+1)!*H(n), where H(n) is the harmonic number. - G. C. Greubel, Dec 02 2019

Example

Triangle begins as:
      4;
      9,     9;
     32,    24,    32;
    150,   100,   100,   150;
    864,   540,   480,   540,   864;
   5880,  3528,  2940,  2940,  3528,  5880;
  46080, 26880, 21504, 20160, 21504, 26880, 46080;

Maple

seq(seq( (n+1)*(n+1)!/(k*(n-k+1)), k=1..n), n=1..10); # G. C. Greubel, Dec 02 2019

Mathematica

Table[(n+1)*(n+1)!/(k*(n-k+1)), {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Dec 02 2019 *)

Prog

(PARI) T(n, k) = (n+1)*(n+1)!/(k*(n-k+1)); \\ G. C. Greubel, Dec 02 2019
(Magma) [(n+1)*Factorial(n+1)/(k*(n-k+1)): k in [1..n], n in [1..10]]; // G. C. Greubel, Dec 02 2019
(Sage) [[(n+1)*factorial(n+1)/(k*(n-k+1)) for k in (1..n)] for n in (1..10)] # G. C. Greubel, Dec 02 2019
(GAP) Flat(List([1..10], n-> List([1..n], k-> (n+1)*Factorial(n+1)/(k*(n-k+1)) ))); # G. C. Greubel, Dec 02 2019

Crossrefs

Cf. A001008, A002805, A052517, A058298.

Sequence in context: A177083 A081949 A091657 * A171001 A088037 A071768

Adjacent sequences: A156044 A156045 A156046 * A156048 A156049 A156050

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Feb 02 2009

Extensions

Offset changed by G. C. Greubel, Dec 02 2019

Status

approved