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URL: https://oeis.org/A027798

⇱ A027798 - OEIS

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A027798
a(n) = 26*(n+1)*binomial(n+3,13).
1
286, 4368, 35490, 203840, 928200, 3564288, 11992344, 36279360, 100524060, 258658400, 624660036, 1427794368, 3109779400, 6489974400, 13037895000, 25310900160, 47640468330, 87185170800, 155514818550, 270951408000, 461972150640, 772082488320, 1266697832400
OFFSET
10,1
COMMENTS
Number of 17-subsequences of [ 1, n ] with just 3 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
FORMULA
G.f.: 26*(11+3x)*x^10/(1-x)^15.
a(n) = C(n+1, 11)*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>=10} 1/a(n) = 11*Pi^2/2 - 631938577/11642400.
Sum_{n>=10} (-1)^n/a(n) = 11*Pi^2/4 + 69632*log(2)/105 - 5667600943/11642400. (End)
MATHEMATICA
Table[26*(n+1)*Binomial[n+3, 13], {n, 10, 30}] (* Harvey P. Dale, Jan 23 2012 *)
Table[Binomial[n + 1, 11] Binomial[n + 3, 3], {n, 10, 32}] (* Michael De Vlieger, Mar 16 2016 *)
CROSSREFS
Sequence in context: A204035 A235409 A238251 * A072817 A117994 A221431
KEYWORD
nonn
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved