login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137260 Triangle T(n, k) = k*(n-1)! - k!, read by rows. 2
0, 0, 0, 1, 2, 0, 5, 10, 12, 0, 23, 46, 66, 72, 0, 119, 238, 354, 456, 480, 0, 719, 1438, 2154, 2856, 3480, 3600, 0, 5039, 10078, 15114, 20136, 25080, 29520, 30240, 0, 40319, 80638, 120954, 161256, 201480, 241200, 277200, 282240, 0, 362879, 725758, 1088634, 1451496, 1814280, 2176560, 2535120, 2862720, 2903040, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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

Sum_{k=1..n} T(n, k) = ((n+1)! - 2*!(n+1))/2 = (A000142(n+1) - 2*(A003422(n+1) -1))/2 = (A000142(n+1) - 2*(A007489(n) - 2))/2. - G. C. Greubel, Apr 10 2021

EXAMPLE

Triangle begins as:

       0;

       0,      0;

       1,      2,       0;

       5,     10,      12,       0;

      23,     46,      66,      72,       0;

     119,    238,     354,     456,     480,       0;

     719,   1438,    2154,    2856,    3480,    3600,       0;

    5039,  10078,   15114,   20136,   25080,   29520,   30240,       0;

   40319,  80638,  120954,  161256,  201480,  241200,  277200,  282240,       0;

  362879, 725758, 1088634, 1451496, 1814280, 2176560, 2535120, 2862720, 2903040, 0;

MAPLE

A137260:= (n, k) -> k*((n-1)! - (k-1)!); seq(seq(A137260(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 10 2021

MATHEMATICA

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

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

PROG

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

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

CROSSREFS

Cf. A000142, A007489.

Sequence in context: A002976 A292590 A080901 * A263101 A219765 A153059

Adjacent sequences:  A137257 A137258 A137259 * A137261 A137262 A137263

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Mar 11 2008

EXTENSIONS

Edited by G. C. Greubel, Apr 10 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)