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%I #10 Sep 08 2022 08:46:04
%S 1,11,1,121,22,2,1331,363,66,6,14641,5324,1452,264,24,161051,73205,
%T 26620,7260,1320,120,1771561,966306,439230,159720,43560,7920,720,
%U 19487171,12400927,6764142,3074610,1118040,304920,55440,5040,214358881
%N Triangle, read by rows, where T(n,k) = k!*C(n, k)*11^(n-k) for n>=0, k=0..n.
%C Triangle formed by the derivatives of x^n evaluated at x=11. Also:
%C first column: A001020;
%C second column: A081127;
%C third column: 2*A081141.
%H Vincenzo Librandi, <a href="/A218018/b218018.txt">Rows n = 0..100, flattened</a>
%F T(n,k) = 11^(n-k)*n!/(n-k)! for n>=0, k=0..n.
%F E.g.f. (by columns): exp(11*x)*x^k.
%e Triangle begins:
%e 1;
%e 11, 1;
%e 121, 22, 2;
%e 1331, 363, 66, 6;
%e 14641, 5324, 1452, 264, 24;
%e 161051, 73205, 26620, 7260, 1320, 120;
%e 1771561, 966306, 439230, 159720, 43560, 7920, 720;
%e 19487171, 12400927, 6764142, 3074610, 1118040, 304920, 55440, 5040; etc.
%t Flatten[Table[n!/(n-k)! * 11^(n-k), {n, 0, 10}, {k, 0, n}]]
%o (Magma) [Factorial(n)/Factorial(n-k)*11^(n-k): k in [0..n], n in [0..10]];
%Y Cf. A001020, A081127, A081141, A217629, A218016, A218017.
%K nonn,tabl,easy
%O 0,2
%A _Vincenzo Librandi_, Nov 17 2012
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