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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. 1

%I

%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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Last modified April 24 16:06 EDT 2019. Contains 322430 sequences. (Running on oeis4.)