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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

%I

%S 1,7,1,49,14,2,343,147,42,6,2401,1372,588,168,24,16807,12005,6860,

%T 2940,840,120,117649,100842,72030,41160,17640,5040,720,823543,823543,

%U 705894,504210,288120,123480,35280,5040,5764801,6588344,6588344,5647152,4033680,2304960,987840,282240,40320

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

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

%C first column: A000420;

%C second column: A027473;

%C third column: 2*A027474;

%C fourth column: 6*A140107.

%H Vincenzo Librandi, <a href="/A218017/b218017.txt">Rows n = 0..100, flattened</a>

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

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

%e Triangle begins:

%e 1;

%e 7, 1;

%e 49, 14, 2;

%e 343, 147, 42, 6;

%e 2401, 1372, 588, 168, 24;

%e 16807, 12005, 6860, 2940, 840, 120;

%e 117649, 100842, 72030, 41160, 17640, 5040, 720;

%e 823543, 823543, 705894, 504210, 288120, 123480, 35280, 5040; etc.

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

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

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

%K nonn,tabl,easy

%O 0,2

%A _Vincenzo Librandi_, Nov 10 2012

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Last modified May 25 19:44 EDT 2019. Contains 323576 sequences. (Running on oeis4.)