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A027802
a(n) = 5*(n+1)*binomial(n+4,6).
0
15, 140, 700, 2520, 7350, 18480, 41580, 85800, 165165, 300300, 520520, 866320, 1392300, 2170560, 3294600, 4883760, 7088235, 10094700, 14132580, 19481000, 26476450, 35521200, 47092500, 61752600, 80159625, 103079340, 131397840, 166135200, 208460120, 259705600
OFFSET
2,1
COMMENTS
Number of 11-subsequences of [ 1, n ] with just 4 contiguous pairs.
FORMULA
G.f.: 5*(3+4x)*x^2/(1-x)^8.
a(n) = C(n+1, 3)*C(n+4, 4) - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=2} 1/a(n) = 2*Pi^2 - 5899/300.
Sum_{n>=2} (-1)^n/a(n) = Pi^2 - 64*log(2)/5 - 281/300. (End)
MATHEMATICA
Table[5 * (n+1) * Binomial[n+4, 6], {n, 2, 50}] (* Amiram Eldar, Feb 04 2022 *)
CROSSREFS
Sequence in context: A225978 A175707 A123955 * A302855 A133716 A035330
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved