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Search: id:A136214
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| A136214 |
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Triangle U, read by rows, where U(n,k) = Product_{j=k..n-1} (3*j+1) for n>k with U(n,n) = 1. |
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+0
3
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| 1, 1, 1, 4, 4, 1, 28, 28, 7, 1, 280, 280, 70, 10, 1, 3640, 3640, 910, 130, 13, 1, 58240, 58240, 14560, 2080, 208, 16, 1, 1106560, 1106560, 276640, 39520, 3952, 304, 19, 1, 24344320, 24344320, 6086080, 869440, 86944, 6688, 418, 22, 1
(list; table; graph; listen)
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OFFSET
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0,4
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FORMULA
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Matrix powers: column 0 of U^(k+1) = column k of A136216 for k>=0; simultaneously, column k = column 0 of A136216^(3k+1) for k>=0. Element in column 0, row n, of matrix power U^(k+1) = A007559(n)*C(n+k,k), where A007559 are triple factorials found in column 0 of this triangle.
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EXAMPLE
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Triangle begins:
1;
1, 1;
4, 4, 1;
28, 28, 7, 1;
280, 280, 70, 10, 1;
3640, 3640, 910, 130, 13, 1;
58240, 58240, 14560, 2080, 208, 16, 1;
1106560, 1106560, 276640, 39520, 3952, 304, 19, 1; ...
Matrix inverse begins:
1;
-1, 1;
0, -4, 1;
0, 0, -7, 1;
0, 0, 0, -10, 1;
0, 0, 0, 0, -13, 1; ...
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PROGRAM
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(PARI) T(n, k)=if(n==k, 1, prod(j=k, n-1, 3*j+1))
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CROSSREFS
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Cf. A112333, A136216, A136239; A007559, A136212, A136213.
Adjacent sequences: A136211 A136212 A136213 this_sequence A136215 A136216 A136217
Sequence in context: A116866 A126280 A071207 this_sequence A067328 A111845 A120396
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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), Feb 07 2008
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