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Search: id:A091173
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| A091173 |
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Triangle, read by rows, where the n-th row lists the coefficients of the polynomial of degree n, with root -1, that generates the n-th diagonal of this sequence. |
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+0
3
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| 1, 1, 1, 1, 2, 1, 2, 4, 3, 1, 4, 10, 9, 4, 1, 10, 28, 30, 16, 5, 1, 30, 90, 108, 68, 25, 6, 1, 106, 328, 426, 304, 130, 36, 7, 1, 420, 1338, 1842, 1444, 700, 222, 49, 8, 1, 1818, 6024, 8706, 7320, 3930, 1404, 350, 64, 9, 1, 8530, 29626, 44736, 39700, 23110, 9150, 2548
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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The left-most column (A091174) is determined by the condition that the root of each row polynomial is -1. The next column is T(n,1)=A091175(n+1) (n>=0).
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FORMULA
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T(n+k, k) = Sum T(n, j)*k^j {j=0..n}, with T(0, 0)=1, T(0, n)=1, and T(n, 0) = -sum T(n, j)*(-1)^j {j=1..n}.
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EXAMPLE
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For row n=3, k=2, T(n+k,k)=T(5,2)=30=(2)+(4)2+(3)2^2+(1)2^3.
For n=4, k=3, T(n+k,k)=T(7,3)=304=(4)+(10)3+(9)3^2+(4)3^3+(1)3^4.
Rows begin with n=0:
{1},
{1,1},
{1,2,1},
{2,4,3,1},
{4,10,9,4,1},
{10,28,30,16,5,1},
{30,90,108,68,25,6,1},
{106,328,426,304,130,36,7,1},
{420,1338,1842,1444,700,222,49,8,1},
{1818,6024,8706,7320,3930,1404,350,64,9,1},...
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CROSSREFS
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Cf. A091174, A091175.
Adjacent sequences: A091170 A091171 A091172 this_sequence A091174 A091175 A091176
Sequence in context: A079878 A137406 A120855 this_sequence A101897 A078142 A133422
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 25 2003
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