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Search: id:A115080
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| A115080 |
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Triangle, read by rows, where T(n,k) equals the dot product of the vector of terms in row n that are to the right of T(n,k) with the vector of terms in column k that are above T(n,k): T(n,k) = Sum_{j=0..n-k-1} T(n,j+k+1)*T(j+k,k) for n>k+1>0, with T(n,n) = 1 and T(n,n-1) = n (n>=1). |
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+0
8
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| 1, 1, 1, 3, 2, 1, 11, 5, 3, 1, 50, 20, 7, 4, 1, 257, 94, 31, 9, 5, 1, 1467, 507, 150, 44, 11, 6, 1, 9081, 3009, 853, 218, 59, 13, 7, 1, 60272, 19350, 5251, 1307, 298, 76, 15, 8, 1, 424514, 132920, 35109, 8313, 1881, 390, 95, 17, 9, 1, 3151226, 966962, 249332
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Triangle A115085 is the dual of this triangle.
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EXAMPLE
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T(n,k)=[T(n,k+1),T(n,k+2),..,T(n,n)]*[T(k,k),T(k+1,k),..,T(n-1,k)]:
11 = [5,3,1]*[1,1,3] = 5*1 + 3*1 + 1*3;
20 = [7,4,1]*[1,2,5] = 7*1 + 4*2 + 1*5;
94 = [31,9,5,1]*[1,2,5,20] = 31*1 + 9*2 + 5*5 + 1*20;
150 = [44,11,6,1]*[1,3,7,31] = 44*1 + 11*3 + 6*7 + 1*31.
Triangle begins:
1;
1,1;
3,2,1;
11,5,3,1;
50,20,7,4,1;
257,94,31,9,5,1;
1467,507,150,44,11,6,1;
9081,3009,853,218,59,13,7,1;
60272,19350,5251,1307,298,76,15,8,1;
424514,132920,35109,8313,1881,390,95,17,9,1;
3151226,966962,249332,57738,12315,2587,494,116,19,10,1; ...
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PROGRAM
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(PARI) {T(n, k)=if(n==k, 1, if(n==k+1, n, sum(j=0, n-k-1, T(n, j+k+1)*T(j+k, k))))}
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CROSSREFS
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Cf. A115081 (column 0), A115082 (column 1), A115083 (column 2), A115084 (row sums); A115085 (dual triangle).
Sequence in context: A101894 A116071 A077756 this_sequence A104219 A123513 A117442
Adjacent sequences: A115077 A115078 A115079 this_sequence A115081 A115082 A115083
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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 13 2006
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