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URL: https://oeis.org/A027801

⇱ A027801 - OEIS

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A027801
a(n) = 5*(n+1)*binomial(n+4,5)/2.
3
5, 45, 210, 700, 1890, 4410, 9240, 17820, 32175, 55055, 90090, 141960, 216580, 321300, 465120, 658920, 915705, 1250865, 1682450, 2231460, 2922150, 3782350, 4843800, 6142500, 7719075, 9619155, 11893770, 14599760, 17800200, 21564840, 25970560, 31101840, 37051245
OFFSET
1,1
COMMENTS
Number of 10-subsequences of [ 1, n ] with just 4 contiguous pairs.
FORMULA
G.f.: 5*(1+2x)*x/(1-x)^7.
a(n) = C(n+1, 2)*C(n+4, 4) - Zerinvary Lajos, May 10 2005, corrected by R. J. Mathar, Feb 13 2016
a(n) = 5*A051923(n-1).
From Amiram Eldar, Jan 28 2022: (Start)
Sum_{n>=1} 1/a(n) = 241/18 - 4*Pi^2/3.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi^2/3 - 64*log(2)/3 + 151/18. (End)
MATHEMATICA
Table[5(n+1) Binomial[n+4, 5]/2, {n, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {5, 45, 210, 700, 1890, 4410, 9240}, 30] (* Harvey P. Dale, Dec 13 2014 *)
CROSSREFS
Cf. A051923.
Sequence in context: A302726 A201876 A351426 * A079139 A269911 A249638
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved