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A218018 Triangle, read by rows, where T(n,k) = k!*C(n, k)*11^(n-k) for n>=0, k=0..n.

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