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A218018
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Triangle, read by rows, where T(n,k) = k!*C(n, k)*11^(n-k) for n>=0, k=0..n.
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1
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1, 11, 1, 121, 22, 2, 1331, 363, 66, 6, 14641, 5324, 1452, 264, 24, 161051, 73205, 26620, 7260, 1320, 120, 1771561, 966306, 439230, 159720, 43560, 7920, 720, 19487171, 12400927, 6764142, 3074610, 1118040, 304920, 55440, 5040, 214358881
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OFFSET
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0,2
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COMMENTS
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Triangle formed by the derivatives of x^n evaluated at x=11. Also:
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LINKS
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FORMULA
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T(n,k) = 11^(n-k)*n!/(n-k)! for n>=0, k=0..n.
E.g.f. (by columns): exp(11*x)*x^k.
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EXAMPLE
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Triangle begins:
1;
11, 1;
121, 22, 2;
1331, 363, 66, 6;
14641, 5324, 1452, 264, 24;
161051, 73205, 26620, 7260, 1320, 120;
1771561, 966306, 439230, 159720, 43560, 7920, 720;
19487171, 12400927, 6764142, 3074610, 1118040, 304920, 55440, 5040; etc.
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MATHEMATICA
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Flatten[Table[n!/(n-k)! * 11^(n-k), {n, 0, 10}, {k, 0, n}]]
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PROG
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(Magma) [Factorial(n)/Factorial(n-k)*11^(n-k): k in [0..n], n in [0..10]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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