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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 floor(5*(n+1)/2) into exactly 5 positive integers each no more than n.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for sequences related to compositions
Index to sequences with linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).
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FORMULA
| a(n) =(230*n^4+70*n^2+27-(30*n^2+27)*(-1)^n)/384 =A077042(n, 5).
a(n) = +2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8).
G.f.: -x*(1+8*x+29*x^2+39*x^3+29*x^4+8*x^5+x^6) / ( (1+x)^3*(x-1)^5 ). - R. J. Mathar, Sep 04 2011
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EXAMPLE
| a(2)=10 since the compositions of floor(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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PROG
| (MAGMA) [(230*n^4+70*n^2+27-(30*n^2+27)*(-1)^n)/384: n in [0..40]]; // Vincenzo Librandi, Sep 05 2011
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CROSSREFS
| Sequence in context: A106041 A143855 A124162 * A069038 A030183 A135242
Adjacent sequences: A077041 A077042 A077043 * A077045 A077046 A077047
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 22 2002
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