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A027816 a(n) = 66*(n+1)*binomial(n+5,11). 1

%I #24 Feb 03 2022 05:51:37

%S 462,6336,46332,240240,990990,3459456,10618608,29405376,74826180,

%T 177365760,395747352,838053216,1695505812,3294910080,6177956400,

%U 11218384320,19791524610,34015101120,57085528500,93740446800,150886065330,238437239040,370429282080

%N a(n) = 66*(n+1)*binomial(n+5,11).

%C Number of 17-subsequences of [ 1, n ] with just 5 contiguous pairs.

%H T. D. Noe, <a href="/A027816/b027816.txt">Table of n, a(n) for n = 6..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F G.f.: 66*(7+5x)*x^6/(1-x)^13.

%F a(n) = C(n+1, 7)*C(n+5, 5). - _Zerinvary Lajos_, May 26 2005; corrected by _R. J. Mathar_, Feb 10 2016

%F a(n)= 13*a(n-1)- 78*a(n-2)+ 286*a(n-3)-715*a(n-4)+1287*a(n-5)- 1716*a(n-6)+ 1716*a(n-7)- 1287*a(n-8)+ 715*a(n-9)- 286*a(n-10)+ 78*a(n-11)-13*a(n-12)+a (n-13). - _Harvey P. Dale_, Dec 27 2015

%F From _Amiram Eldar_, Feb 03 2022: (Start)

%F Sum_{n>=6} 1/a(n) = 35*Pi^2/6 - 10445563/181440.

%F Sum_{n>=6} (-1)^n/a(n) = 35*Pi^2/12 + 512*log(2)/9 - 12377237/181440. (End)

%t Table[66(n+1)Binomial[n+5,11],{n,6,50}] (* or *) LinearRecurrence[ {13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{462,6336,46332,240240,990990,3459456,10618608,29405376,74826180,177365760,395747352,838053216,1695505812},40] (* _Harvey P. Dale_, Dec 27 2015 *)

%K nonn,easy

%O 6,1

%A Thi Ngoc Dinh (via _R. K. Guy_)

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)