|
%I #29 Jan 30 2022 04:24:29
%S 13,196,1575,8960,40460,154224,515508,1550400,4273290,10943240,
%T 26313518,59907456,130007500,270415600,541574100,1048380480,
%U 1968053535,3592795500,6393845325,11115955200,18914492520,31551447840,51671823000,83188425600,131811290100
%N a(n) = (n+1)*binomial(n+1,13).
%C Number of 15-subsequences of [ 1, n ] with just 1 contiguous pair.
%H T. D. Noe, <a href="/A027773/b027773.txt">Table of n, a(n) for n = 12..1000</a>
%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F G.f.: (13+x)*x^12/(1-x)^15.
%F From _Amiram Eldar_, Jan 30 2022: (Start)
%F Sum_{n>=12} 1/a(n) = 13*Pi^2/6 - 8183956651/384199200.
%F Sum_{n>=12} (-1)^n/a(n) = 13*Pi^2/12 + 34451456*log(2)/3465 - 2651886676309/384199200. (End)
%t (#+1)Binomial[#+1,13]&/@Range[12,40] (* _Harvey P. Dale_, Mar 18 2011 *)
%K nonn,easy
%O 12,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
|
