%I #37 Sep 08 2022 08:46:04
%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