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Search: id:A124430
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| 1, 1, 2, 3, 7, 13, 31, 61, 144, 296, 714, 1534, 3761, 8303, 20495, 46115, 114461, 261445, 651114, 1503207, 3749017, 8726147, 21788311, 51072555, 127698665, 301244477, 754496298, 1790598079, 4494019431, 10726676701, 26983034009
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=0..[n/2]} a(k)*C([n/2],k)*C([(n+1)/2],k) for n>0, with a(0)=1.
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EXAMPLE
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a(5) = 1*a(0) + 6*a(1) + 3*a(2) = 1*1 + 6*1 + 3*2 = 13;
a(6) = 1*a(0) + 9*a(1) + 9*a(2) + 1*a(3) = 1*1 + 9*1 + 9*2 + 1*3 = 31.
Triangle A124428(n,k) = C([n/2],k)*C([(n+1)/2],k) 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; ...
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, a(k)*binomial(n\2, k)*binomial((n+1)\2, k)))}
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CROSSREFS
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Cf. A124428, A124429.
Sequence in context: A071899 A102644 A014234 this_sequence A002013 A003120 A032131
Adjacent sequences: A124427 A124428 A124429 this_sequence A124431 A124432 A124433
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 31 2006
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