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A137259 Triangle T(n, k) = n*( (n-1)! - (k-1)! ), read by rows. 1
0, 0, 0, 3, 3, 0, 20, 20, 16, 0, 115, 115, 110, 90, 0, 714, 714, 708, 684, 576, 0, 5033, 5033, 5026, 4998, 4872, 4200, 0, 40312, 40312, 40304, 40272, 40128, 39360, 34560, 0, 362871, 362871, 362862, 362826, 362664, 361800, 356400, 317520, 0, 3628790, 3628790, 3628780, 3628740, 3628560, 3627600, 3621600, 3578400, 3225600, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Krassimir Penev, The Fubini Principle, The American Mathematical Monthly, Vol. 115, No. 3 (Mar., 2008), pp. 245-248.

FORMULA

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

Sum_{k=1..n} T(n, k) = n*(n! - !n) = n*(n! - A003422(n)). - G. C. Greubel, Apr 10 2021

EXAMPLE

Triangle begins as:

       0;

       0,      0;

       3,      3,      0;

      20,     20,     16,      0;

     115,    115,    110,     90,      0;

     714,    714,    708,    684,    576,      0;

    5033,   5033,   5026,   4998,   4872,   4200,      0;

   40312,  40312,  40304,  40272,  40128,  39360,  34560,      0;

  362871, 362871, 362862, 362826, 362664, 361800, 356400, 317520, 0;

MAPLE

A137259:= (n, k) -> n*((n-1)! - (k-1)!); seq(seq(A137259(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 10 2021

MATHEMATICA

T[n_, k_]:= n! - n*(k-1)!;

Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 10 2021 *)

PROG

(Magma) [n*(Factorial(n-1) - Factorial(k-1)): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 10 2021

(Sage) flatten([[n*(factorial(n-1) - factorial(k-1)) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 10 2021

CROSSREFS

Cf. A003422, A137260.

Sequence in context: A039928 A247889 A309012 * A166553 A285863 A111843

Adjacent sequences:  A137256 A137257 A137258 * A137260 A137261 A137262

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Mar 11 2008

EXTENSIONS

Edited by G. C. Greubel, Apr 10 2021

STATUS

approved

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Last modified October 17 13:16 EDT 2021. Contains 348048 sequences. (Running on oeis4.)