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A218017
Triangle, read by rows, where T(n,k) = k!*C(n, k)*7^(n-k) for n>=0, k=0..n.
4
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
0,2
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.
LINKS
Vincenzo Librandi, Rows n = 0..100, flattened
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.
EXAMPLE
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.
MATHEMATICA
Flatten[Table[n!/(n-k)!*7^(n-k), {n, 0, 10}, {k, 0, n}]]
PROG
(Magma) [Factorial(n)/Factorial(n-k)*7^(n-k): k in [0..n], n in [0..10]];
KEYWORD
nonn,tabl,easy
AUTHOR
Vincenzo Librandi, Nov 10 2012
STATUS
approved