A155162 Triangle T(n,k) = binomial(n, k)*(k! + (n-k)!), read by rows.

2, 2, 2, 3, 4, 3, 7, 9, 9, 7, 25, 28, 24, 28, 25, 121, 125, 80, 80, 125, 121, 721, 726, 390, 240, 390, 726, 721, 5041, 5047, 2562, 1050, 1050, 2562, 5047, 5041, 40321, 40328, 20216, 7056, 3360, 7056, 20216, 40328, 40321, 362881, 362889, 181512, 60984, 18144, 18144, 60984, 181512, 362889, 362881

Offset: 0

Author

Roger L. Bagula, Jan 21 2009

Keywords

• nonn
• tabl

Examples

			Triangle begins as:
       2;
       2,      2;
       3,      4,      3;
       7,      9,      9,     7;
      25,     28,     24,    28,    25;
     121,    125,     80,    80,   125,   121;
     721,    726,    390,   240,   390,   726,   721;
    5041,   5047,   2562,  1050,  1050,  2562,  5047,   5041;
   40321,  40328,  20216,  7056,  3360,  7056, 20216,  40328,  40321;
  362881, 362889, 181512, 60984, 18144, 18144, 60984, 181512, 362889, 362881;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A000522, A054091.

Programs

Magma

[Binomial(n,k)*(Factorial(k) + Factorial(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 19 2021

Maple

A155162:= (n,k)-> binomial(n,k)*(k! + (n-k)!); seq(seq(A155162(n,k), k=0..n), n=0..12); # G. C. Greubel, Mar 19 2021

Mathematica

Table[Binomial[n,k](k! +(n-k)!), {n,0,12},{k,0,n}]//Flatten

Sage

flatten([[binomial(n,k)*(factorial(k) + factorial(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 19 2021

Formula

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

Sum_{k=0..n} T(n, k) = 2*A000522(n) = A054091(n+1). - G. C. Greubel, Mar 19 2021

Extensions

Edited by G. C. Greubel, Mar 19 2021