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A027796
a(n) = 55*(n+1)*binomial(n+3,11)/3.
1
165, 2200, 15730, 80080, 325325, 1121120, 3403400, 9335040, 23556390, 55426800, 122862740, 258658400, 520550030, 1006778080, 1879537000, 3399510400, 5975701875, 10236025800, 17125658550, 28042014000, 45017447475, 70963464000, 109993369200, 167844019200
OFFSET
8,1
COMMENTS
Number of 15-subsequences of [ 1, n ] with just 3 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
G.f.: 55*(3+x)*x^8/(1-x)^13.
a(n) = C(n+1, 9)*C(n+3, 3). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 01 2022: (Start)
Sum_{n>=8} 1/a(n) = 9*Pi^2/2 - 5222219/117600.
Sum_{n>=8} (-1)^n/a(n) = 9*Pi^2/4 + 9216*log(2)/35 - 8024887/39200. (End)
MATHEMATICA
Table[55 (n + 1) Binomial[n + 3, 11]/3, {n, 8, 31}] (* or *) Table[Binomial[n + 1, 9] Binomial[n + 3, 3], {n, 8, 31}] (* Michael De Vlieger, Mar 16 2016 *)
CROSSREFS
Sequence in context: A225715 A066177 A184490 * A145055 A194483 A105944
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved