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Search: id:A097084
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| A097084 |
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Triangle, read by rows, where the n-th diagonal equals the n-th row transformed by triangle A008459 (squared binomial coefficients). |
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+0
2
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| 1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 10, 10, 1, 1, 5, 18, 28, 17, 1, 1, 6, 27, 74, 69, 26, 1, 1, 7, 39, 137, 245, 151, 37, 1, 1, 8, 52, 236, 586, 676, 298, 50, 1, 1, 9, 68, 372, 1194, 2126, 1634, 540, 65, 1, 1, 10, 85, 552, 2322, 5152, 6620, 3578, 913, 82, 1, 1, 11, 105, 777
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums form A097085.
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FORMULA
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T(n, k) = Sum_{j=0..k} T(n-k, j)*C(k, j)^2.
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EXAMPLE
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T(8,3) = 236 = (1)*1^2 + (5)*3^2 + (18)*3^2 + (28)*1^2
= Sum_{j=0..3} T(5,j)*C(3,j)^2.
Rows begin:
[1],
[1,1],
[1,2,1],
[1,3,5,1],
[1,4,10,10,1],
[1,5,18,28,17,1],
[1,6,27,74,69,26,1],
[1,7,39,137,245,151,37,1],
[1,8,52,236,586,676,298,50,1],...
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PROGRAM
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(PARI) T(n, k)=if(n<k|k<0, 0, if(n==k|k==0, 1, sum(j=0, n-k, T(n-k, j)*binomial(k, j)^2)))
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CROSSREFS
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Cf. A097085, A008459.
Sequence in context: A135722 A049513 A121207 this_sequence A143327 A094954 A083064
Adjacent sequences: A097081 A097082 A097083 this_sequence A097085 A097086 A097087
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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), Jul 23 2004
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