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A027764
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a(n) = (n+1)*binomial(n+1,4).
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2
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4, 25, 90, 245, 560, 1134, 2100, 3630, 5940, 9295, 14014, 20475, 29120, 40460, 55080, 73644, 96900, 125685, 160930, 203665, 255024, 316250, 388700, 473850, 573300, 688779, 822150, 975415, 1150720, 1350360, 1576784, 1832600, 2120580, 2443665, 2804970, 3207789
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OFFSET
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3,1
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COMMENTS
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Number of 6-subsequences of [ 1, n ] with just 1 contiguous pair.
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LINKS
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FORMULA
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G.f.: (4+x)*x^3/(1-x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Harvey P. Dale, Jun 14 2013
a(n) = 10*C(n+2,2)*C(n+2,5)/(n+2)^2. - Gary Detlefs, Aug 20 2013
Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/3 + 80*log(2)/3 - 194/9. - Amiram Eldar, Jan 28 2022
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MATHEMATICA
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Table[(n + 1)Binomial[n + 1, 4], {n, 3, 40}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {4, 25, 90, 245, 560, 1134}, 40] (* Harvey P. Dale, Jun 14 2013 *)
CoefficientList[Series[(4 + x)/(1 - x)^6, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 08 2014 *)
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PROG
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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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