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A176151 Triangle T(n, k) = 2*(n+1 - mod(n, k+1) - mod(n, n-k+1) ) + (n! - k! - (n-k)!) read by rows. 3
1, 1, 1, 1, 6, 1, 1, 9, 9, 1, 1, 27, 26, 27, 1, 1, 105, 118, 118, 105, 1, 1, 613, 706, 714, 706, 613, 1, 1, 4333, 4930, 5016, 5016, 4930, 4333, 1, 1, 35297, 39610, 40208, 40278, 40208, 39610, 35297, 1, 1, 322577, 357856, 362168, 362742, 362742, 362168, 357856, 322577, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are: 1, 2, 8, 20, 82, 448, 3354, 28560, 270510, 2810688, 31841122, ...

LINKS

G. C. Greubel, Rows n = 0..100 of the triangle, flattened

FORMULA

T(n, k) = 2*(n+1 - mod(n, k+1) - mod(n, n-k+1) ) + (n! - k! - (n-k)!).

T(n, k) = 2*A176149(n, k) - A155170(n, k). - G. C. Greubel, Feb 07 2021

EXAMPLE

Triangle begins as:

  1;

  1,      1;

  1,      6,      1;

  1,      9,      9,      1;

  1,     27,     26,     27,      1;

  1,    105,    118,    118,    105,      1;

  1,    613,    706,    714,    706,    613,      1;

  1,   4333,   4930,   5016,   5016,   4930,   4333,      1;

  1,  35297,  39610,  40208,  40278,  40208,  39610,  35297,      1;

  1, 322577, 357856, 362168, 362742, 362742, 362168, 357856, 322577, 1;

MATHEMATICA

Table[2*(n+1 -Mod[n, k+1] -Mod[n, n-k+1]) + (n! -k! -(n-k)!), {n, 0, 10}, {k, 0, n}]//Flatten

PROG

(Sage) f=factorial; flatten([[2*(n+1 - n%(k+1) - n%(n-k+1)) + (f(n) -f(k) -f(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 07 2021

(Magma) F:=Factorial;; [2*(n+1 - n mod (k+1) - n mod (n-k+1)) + (F(n) -F(k) -F(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 07 2021

CROSSREFS

Cf. A155170, A176149.

Sequence in context: A143087 A144470 A174377 * A204001 A144395 A046621

Adjacent sequences:  A176148 A176149 A176150 * A176152 A176153 A176154

KEYWORD

nonn,tabl,easy,less

AUTHOR

Roger L. Bagula, Apr 10 2010

EXTENSIONS

Edited by G. C. Greubel, Feb 07 2021

STATUS

approved

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Last modified September 19 22:06 EDT 2021. Contains 347576 sequences. (Running on oeis4.)