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URL: https://oeis.org/A027799

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A027799
a(n) = 91*(n+1)*binomial(n+3,14)/3.
1
364, 5915, 50960, 309400, 1485120, 5996172, 21162960, 67016040, 193993800, 520550030, 1308811504, 3109779400, 7030805600, 15210877500, 31638625200, 63520624440, 123512325300, 233272227825, 429006396000, 769953584400, 1351144354560, 2322279359400, 3915247845600
OFFSET
11,1
COMMENTS
Number of 18-subsequences of [ 1, n ] with just 3 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
FORMULA
G.f.: 91*(4+x)*x^11/(1-x)^16.
a(n) = C(n+1, 12)*C(n+3, 3). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 02 2022: (Start)
Sum_{n>=11} 1/a(n) = 106810320313/1803601800 - 6*Pi^2.
Sum_{n>=11} (-1)^(n+1)/a(n) = 3*Pi^2 + 5341184*log(2)/5005 - 1387532216767/1803601800. (End)
MATHEMATICA
Table[91 (n + 1) Binomial[n + 3, 14]/3, {n, 11, 33}] (* or *) Table[Binomial[n + 1, 12] Binomial[n + 3, 3], {n, 11, 33}] (* Michael De Vlieger, Mar 16 2016 *)
CROSSREFS
Sequence in context: A305184 A105920 A241617 * A115191 A175114 A022045
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved