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A169792
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Expansion of ((1-x)/(1-2x))^5.
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11
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1, 5, 20, 70, 225, 681, 1970, 5500, 14920, 39520, 102592, 261760, 657920, 1632000, 4001280, 9708544, 23336960, 55623680, 131563520, 309002240, 721092608, 1672806400, 3859415040, 8859156480, 20240138240, 46038777856, 104291368960, 235342397440, 529153392640
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of weak compositions of n with exactly 4 parts equal to 0. - Milan Janjic, Jun 27 2010
Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)^5; see A291000. - Clark Kimberling, Aug 24 2017
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LINKS
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FORMULA
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a(n) = 10*a(n-1) - 40*a(n-2) + 80*a(n-3) - 80*a(n-4) + 32*a(n-5), n >= 6. - Vincenzo Librandi, Mar 14 2011
a(n) = 2^n*(n+4)*(n^3 + 26*n^2 + 171*n + 186)/768, n > 0. - R. J. Mathar, Mar 14 2011
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MAPLE
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seq(coeff(series(((1-x)/(1-2*x))^5, x, n+1), x, n), n=0..30); # Muniru A Asiru, Aug 22 2018
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MATHEMATICA
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CoefficientList[Series[((1 - x)/(1 - 2 x))^5, {x, 0, 28}], x] (* Michael De Vlieger, Oct 15 2018 *)
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PROG
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(GAP) Concatenation([1], List([1..30], n->2^n*(n+4)*(n^3+26*n^2+171*n+186)/768)); # Muniru A Asiru, Aug 22 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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