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Search: id:A136630
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| A136630 |
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Unsigned matrix inverse of triangle A121408; related to central factorial numbers. |
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+0
3
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| 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 4, 0, 1, 0, 1, 0, 10, 0, 1, 0, 0, 16, 0, 20, 0, 1, 0, 1, 0, 91, 0, 35, 0, 1, 0, 0, 64, 0, 336, 0, 56, 0, 1, 0, 1, 0, 820, 0, 966, 0, 84, 0, 1, 0, 0, 256, 0, 5440, 0, 2352, 0, 120, 0, 1, 0, 1, 0, 7381, 0, 24970, 0, 5082, 0, 165, 0, 1, 0, 0, 1024, 0, 87296, 0
(list; table; graph; listen)
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OFFSET
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0,13
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FORMULA
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G.f. for column k: x^k/Product_{j=0..[k/2]} (1 - (2j + k-2[k/2])^2 * x^2). G.f. for column 2k: x^(2k)/Product_{j=0..k} (1 - (2j)^2*x^2). G.f. for column 2k+1: x^(2k+1)/Product_{j=0..k} (1 - (2j+1)^2*x^2).
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 0, 1;
0, 1, 0, 1;
0, 0, 4, 0, 1;
0, 1, 0, 10, 0, 1;
0, 0, 16, 0, 20, 0, 1;
0, 1, 0, 91, 0, 35, 0, 1;
0, 0, 64, 0, 336, 0, 56, 0, 1;
0, 1, 0, 820, 0, 966, 0, 84, 0, 1;
0, 0, 256, 0, 5440, 0, 2352, 0, 120, 0, 1;
0, 1, 0, 7381, 0, 24970, 0, 5082, 0, 165, 0, 1; ...
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PROGRAM
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(PARI) {T(n, k)=polcoeff(x^k/prod(j=0, k\2, 1-(2*j+k-2*(k\2))^2*x^2 +x*O(x^n)), n)}
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CROSSREFS
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Cf. A121408; A136631 (antidiagonal sums), A003724 (row sums), A136632; A002452 (column 3), A002453 (column 5); A008958 (central factorial triangle).
Adjacent sequences: A136627 A136628 A136629 this_sequence A136631 A136632 A136633
Sequence in context: A036859 A036861 A120324 this_sequence A111728 A143784 A147311
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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), Jan 14 2008
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