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A027813 a(n) = 14*(n+1)*binomial(n+5,8). 0
56, 630, 3780, 16170, 55440, 162162, 420420, 990990, 2162160, 4424420, 8576568, 15872220, 28217280, 48430620, 80582040, 130423524, 205931880, 317983050, 481180700, 714864150, 1044323280, 1502250750, 2130464700, 2981938050, 4123173600, 5636967336, 7625605680 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
Number of 14-subsequences of [ 1, n ] with just 5 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: 14*(4+5x)*x^3/(1-x)^10.
a(n) = C(n+1, 4)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=3} 1/a(n) = 290341/8820 - 10*Pi^2/3.
Sum_{n>=3} (-1)^(n+1)/a(n) = 5*Pi^2/3 - 128*log(2)/7 - 3683/980. (End)
MATHEMATICA
Table[14 * (n+1) * Binomial[n+5, 8], {n, 3, 50}] (* Amiram Eldar, Feb 04 2022 *)
CROSSREFS
Sequence in context: A234106 A219475 A264212 * A199914 A190535 A190604
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved

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Last modified February 29 21:35 EST 2024. Contains 370428 sequences. (Running on oeis4.)