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A027810
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a(n) = (n+1)*binomial(n+5, 5).
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12
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1, 12, 63, 224, 630, 1512, 3234, 6336, 11583, 20020, 33033, 52416, 80444, 119952, 174420, 248064, 345933, 474012, 639331, 850080, 1115730, 1447160, 1856790, 2358720, 2968875, 3705156, 4587597, 5638528, 6882744, 8347680, 10063592, 12063744, 14384601, 17066028
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OFFSET
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0,2
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COMMENTS
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Number of 11-subsequences of [ 1, n ] with just 5 contiguous pairs.
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REFERENCES
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Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Herbert John Ryser, Combinatorial Mathematics, Carus Mathematical Monographs No. 14, John Wiley and Sons, 1963, pp. 1-8.
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LINKS
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FORMULA
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G.f.: (1+5*x)/(1-x)^7.
Sum_{n>=0} 1/a(n) = 5*Pi^2/6 - 1025/144.
Sum_{n>=0} (-1)^n/a(n) = 5*Pi^2/12 - 160*log(2)/3 + 4865/144. (End)
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MAPLE
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[seq(n*(n-1)*(n-2)*(n-3)*(n-4)^2/5!, n=5..33)]; # Zerinvary Lajos, Oct 19 2006
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MATHEMATICA
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Table[(n+1)Binomial[n+5, 5], {n, 0, 30}] (* Harvey P. Dale, Jul 29 2014 *)
CoefficientList[Series[(1 + 5 x)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 30 2014 *)
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PROG
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(Magma) [(n+1)*Binomial(n+5, 5): n in [0..40]] /* or */ [n*(n-1)*(n-2)*(n-3)*(n-4)^2/120: n in [5..40]]; // Vincenzo Librandi, Jul 30 2014
(Haskell)
a027810 n = (n + 1) * a007318' (n + 5) 5
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CROSSREFS
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Cf. A093563 ((6, 1) Pascal, column m=6).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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