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Search: id:A125080
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| A125080 |
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Triangle, read by rows, defined by T(n,k) = A000108(n-k)*A001147(k)*C(n,2*k), for k=0..[n/2], n>=0, where A000108 is the Catalan numbers and A001147 is the double factorials. |
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+0
2
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| 1, 1, 2, 1, 5, 6, 14, 30, 6, 42, 140, 75, 132, 630, 630, 75, 429, 2772, 4410, 1470, 1430, 12012, 27720, 17640, 1470, 4862, 51480, 162162, 166320, 39690, 16796, 218790, 900900, 1351350, 623700, 39690, 58786, 923780, 4813380, 9909900, 7432425
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Row sums equals A115081, which is column 0 of triangle A115080.
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EXAMPLE
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Table begins:
1;
1;
2, 1;
5, 6;
14, 30, 6;
42, 140, 75;
132, 630, 630, 75;
429, 2772, 4410, 1470;
1430, 12012, 27720, 17640, 1470;
4862, 51480, 162162, 166320, 39690;
16796, 218790, 900900, 1351350, 623700, 39690; ...
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PROGRAM
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(PARI) {T(n, k)=binomial(2*n-2*k, n-k)/(n-k+1)*binomial(2*k, k)*k!/2^k*binomial(n, 2*k)} (PARI) {T(n, k)=(2*n-2*k)!*n!/k!/(n-k)!/(n-k+1)!/(n-2*k)!/2^k}
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CROSSREFS
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Cf. A115081 (row sums), A115080; A000108, A001147.
Sequence in context: A026221 A030740 A095242 this_sequence A143892 A129321 A064642
Adjacent sequences: A125077 A125078 A125079 this_sequence A125081 A125082 A125083
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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), Nov 19 2006
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