A218017 Triangle, read by rows, where T(n,k) = k!*C(n, k)*7^(n-k) for n>=0, k=0..n.

1, 7, 1, 49, 14, 2, 343, 147, 42, 6, 2401, 1372, 588, 168, 24, 16807, 12005, 6860, 2940, 840, 120, 117649, 100842, 72030, 41160, 17640, 5040, 720, 823543, 823543, 705894, 504210, 288120, 123480, 35280, 5040, 5764801, 6588344, 6588344, 5647152, 4033680, 2304960, 987840, 282240, 40320

Offset: 0

Author

Vincenzo Librandi, Nov 10 2012

Keywords

• nonn
• tabl
• easy

Comments

Triangle formed by the derivatives of x^n evaluated at x=7. Also:

first column: A000420;

second column: A027473;

third column: 2*A027474;

fourth column: 6*A140107.

Examples

			Triangle begins:
1;
7,       1;
49,      14,      2;
343,     147,     42,      6;
2401,    1372,    588,     168,     24;
16807,   12005,   6860,    2940,    840,     120;
117649,  100842,  72030,   41160,   17640,   5040,    720;
823543,  823543,  705894,  504210,  288120,  123480,  35280,  5040; etc.
		

Links

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

Crossrefs

Cf. A000420, A027466, A027473, A027474, A090802, A140107, A217629, A218016.

Programs

Magma

[Factorial(n)/Factorial(n-k)*7^(n-k): k in [0..n], n in [0..10]];

Mathematica

Flatten[Table[n!/(n-k)!*7^(n-k), {n, 0, 10}, {k, 0, n}]]

Formula

T(n,k) = 7^(n-k)*n!/(n-k)! for n>=0, k=0..n.

E.g.f. (by columns): exp(7x)*x^k.