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Search: id:A077044
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| A077044 |
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Largest coefficient in expansion of (1+x+x^2+...+x^(n-1))^5=((1-x^n)/(1-x))^5, i.e. the coefficient of x^floor[5(n-1)/2] and of x^ceiling[5(n-1)/2]; also number of compositions of [5(n+1)/2] into exactly 5 positive integers each no more than n. |
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+0
3
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| 0, 1, 10, 51, 155, 381, 780, 1451, 2460, 3951, 6000, 8801, 12435, 17151, 23030, 30381, 39280, 50101, 62910, 78151, 95875, 116601, 140360, 167751, 198780, 234131, 273780, 318501, 368235, 423851, 485250, 553401, 628160, 710601, 800530
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OFFSET
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0,3
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LINKS
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Index entries for sequences related to compositions
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FORMULA
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a(n) =(230*n^4+70*n^2+27-(30*n^2+27)*(-1)^n)/384 =A077042(n, 5).
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EXAMPLE
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a(2)=10 since the compositions of [5*(2+1)/2]=7 into exactly 5 positive integers each no more than 2 are: 1+1+1+2+2, 1+1+2+1+2, 1+1+2+2+1, 1+2+1+1+2, 1+2+1+2+1, 1+2+2+1+1, 2+1+1+1+2, 2+1+1+2+1, 2+1+2+1+1, 2+2+1+1+1.
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CROSSREFS
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Sequence in context: A072296 A106041 A124162 this_sequence A069038 A030183 A135242
Adjacent sequences: A077041 A077042 A077043 this_sequence A077045 A077046 A077047
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Oct 22 2002
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