A218018 Triangle, read by rows, where T(n,k) = k!*C(n, k)*11^(n-k) for n>=0, k=0..n.

1, 11, 1, 121, 22, 2, 1331, 363, 66, 6, 14641, 5324, 1452, 264, 24, 161051, 73205, 26620, 7260, 1320, 120, 1771561, 966306, 439230, 159720, 43560, 7920, 720, 19487171, 12400927, 6764142, 3074610, 1118040, 304920, 55440, 5040, 214358881

Offset: 0

Author

Vincenzo Librandi, Nov 17 2012

Keywords

• nonn
• tabl
• easy

Comments

Triangle formed by the derivatives of x^n evaluated at x=11. Also:

first column: A001020;

second column: A081127;

third column: 2*A081141.

Examples

			Triangle begins:
1;
11,       1;
121,      22,       2;
1331,     363,      66,      6;
14641,    5324,     1452,    264,     24;
161051,   73205,    26620,   7260,    1320,    120;
1771561,  966306,   439230,  159720,  43560,   7920,   720;
19487171, 12400927, 6764142, 3074610, 1118040, 304920, 55440, 5040; etc.
		

Links

• Vincenzo Librandi, Rows n = 0..100, flattened

Crossrefs

Cf. A001020, A081127, A081141, A217629, A218016, A218017.

Programs

Magma

[Factorial(n)/Factorial(n-k)*11^(n-k): k in [0..n], n in [0..10]];

Mathematica

Flatten[Table[n!/(n-k)! * 11^(n-k), {n, 0, 10}, {k, 0, n}]]

Formula

T(n,k) = 11^(n-k)*n!/(n-k)! for n>=0, k=0..n.

E.g.f. (by columns): exp(11*x)*x^k.