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A027788 a(n) = 15*(n+1)*binomial(n+2,15)/2. 1

%I #31 Jan 12 2023 14:02:34

%S 105,1800,16320,104040,523260,2209320,8139600,26860680,80901810,

%T 225544440,588376800,1448655000,3389852700,7582037400,16287339600,

%U 33738060600,67621543875,131530532400,248917996800,459351961200,828225505800,1461574422000,2528333935200

%N a(n) = 15*(n+1)*binomial(n+2,15)/2.

%C Number of 18-subsequences of [ 1, n ] with just 2 contiguous pairs.

%H T. D. Noe, <a href="/A027788/b027788.txt">Table of n, a(n) for n = 13..1000</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680, -2380, 6188,-12376,19448,-24310,24310,-19448,12376, -6188,2380,-680,136, -17,1).

%F G.f.: 15*(7+x)*x^13/(1-x)^17.

%F a(n) = C(n+1, 14)*C(n+2, 2). - _Zerinvary Lajos_, Apr 28 2005; corrected by _R. J. Mathar_, Mar 16 2016

%F From _Amiram Eldar_, Feb 01 2022: (Start)

%F Sum_{n>=13} 1/a(n) = 15261223009/331273800 - 14*Pi^2/3.

%F Sum_{n>=13} (-1)^(n+1)/a(n) = 7*Pi^2/3 + 40484864*log(2)/6435 - 10165792859017/2318916600. (End)

%t Table[15 (n + 1) Binomial[n + 2, 15]/2, {n, 13, 40}] (* or *) Table[Binomial[n + 1, 14] Binomial[n + 2, 2], {n, 13, 40}] (* _Michael De Vlieger_, Mar 16 2016 *)

%t LinearRecurrence[{17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1},{105,1800,16320,104040,523260,2209320,8139600,26860680,80901810,225544440,588376800,1448655000,3389852700,7582037400,16287339600,33738060600,67621543875},30] (* _Harvey P. Dale_, Jan 12 2023 *)

%K nonn,easy

%O 13,1

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

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)