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Search: id:A080419
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| A080419 |
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Triangle of generalized Chebyshev coefficients. |
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+0
6
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| 1, 4, 1, 15, 7, 1, 54, 36, 10, 1, 189, 162, 66, 13, 1, 648, 675, 360, 105, 16, 1, 2187, 2673, 1755, 675, 153, 19, 1, 7290, 10206, 7938, 3780, 1134, 210, 22, 1, 24057, 37908, 34020, 19278, 7182, 1764, 276, 25, 1, 78732, 137781, 139968, 91854, 40824, 12474, 2592
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Second binomial transform of 'pruned' Pascal triangle Binomial(i+1,j+1), (i,j>=0). Columns include A006234, A080420, A080421, A080422, A080423.
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FORMULA
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T(n, 1)=A006234(n), T(n, k)=0, k>n, T(n, n) = 1. T(n, k)=T(n-1, k-1)+3T(n-1, k) As a square array, it is generated by T1(n, k)= (n+3k)3^n Product{j=1..(k-1), n+j}/(3k(k-1)!) (k>=1, n>=0)
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EXAMPLE
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Rows are {1}, {4,1}, {15,7,1}, {54,36,10,1}, {189,162,66,13,1}, ... For example, 10 = 7+3*1, 66 = 36+3*10.
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CROSSREFS
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Adjacent sequences: A080416 A080417 A080418 this_sequence A080420 A080421 A080422
Sequence in context: A164794 A107873 A156290 this_sequence A095307 A159764 A124029
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 19 2003
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