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Search: id:A124428
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| A124428 |
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Triangle, read by rows: T(n,k) = C([n/2],k)*C([(n+1)/2],k). |
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+0
7
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| 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 6, 3, 1, 9, 9, 1, 1, 12, 18, 4, 1, 16, 36, 16, 1, 1, 20, 60, 40, 5, 1, 25, 100, 100, 25, 1, 1, 30, 150, 200, 75, 6, 1, 36, 225, 400, 225, 36, 1, 1, 42, 315, 700, 525, 126, 7, 1, 49, 441, 1225, 1225, 441, 49, 1, 1, 56, 588, 1960, 2450, 1176, 196, 8
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Row sums form A001405, the central binomial coefficients: C(n,floor(n/2)). The eigenvector of this triangle is A124430.
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FORMULA
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A056953(n) = Sum_{k=0..[n/2]} k!*T(n,k). A026003(n) = Sum_{k=0..[n/2]} 2^k*T(n,k).
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EXAMPLE
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Triangle begins:
1;
1;
1, 1;
1, 2;
1, 4, 1;
1, 6, 3;
1, 9, 9, 1;
1, 12, 18, 4;
1, 16, 36, 16, 1;
1, 20, 60, 40, 5;
1, 25, 100, 100, 25, 1;
1, 30, 150, 200, 75, 6;
1, 36, 225, 400, 225, 36, 1; ...
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PROGRAM
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(PARI) T(n, k)=binomial(n\2, k)*binomial((n+1)\2, k)
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CROSSREFS
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Cf. A001405 (row sums), A056953, A026003, A124429 (antidiagonal sums), A124430 (eigenvector).
Sequence in context: A118745 A131034 A130313 this_sequence A124845 A127625 A124844
Adjacent sequences: A124425 A124426 A124427 this_sequence A124429 A124430 A124431
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KEYWORD
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nonn,tabf
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 31 2006
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