|
%I #16 Apr 27 2020 06:27:16
%S 1,2,7,34,193,1036,5059,23094,101329,434908,1843411,7753582,32441017,
%T 135195464,561615643,2326740526,9617257185,39671268460,163352388259,
%U 671559953358,2756930503801,11303415274600,46290177094635,189368906606254,773942488241473,3160265160763176
%N a(n) = 1 + n*binomial(2*n,n) - n^2*(n^2 - 2*n + 3)/2.
%H Andrew Howroyd, <a href="/A289720/b289720.txt">Table of n, a(n) for n = 0..500</a>
%H A. Umar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Umar/umar2.html">Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations</a>, J. Int. Seq. 14 (2011) # 11.7.5, corollary 42, tables 4.3 and 4.4
%F (n-1)*(69642*n - 248963)*a(n) + (-358060*n^2 + 1078397*n - 66480)*a(n-1) + 3*(56652*n^2 + 710433*n - 1732769)*a(n-2) + (749910*n^2 - 7663147*n + 14398378)*a(n-3) - 2*(157862*n - 346287)*(2*n - 7)*a(n-4) = 0.
%p seq(n*binomial(2*n,n)+1-n^2*(n^2-2*n+3)/2,n=0..20) ;
%o (GAP)
%o A289720:=List([0..10^3], n->1+n*Binomial(2*n,n)-(n^2*(n^2-2*n+3))/2); # _Muniru A Asiru_, Sep 03 2017
%o (PARI) a(n) = {1 + n*binomial(2*n,n) - n^2*(n^2 - 2*n + 3)/2} \\ _Andrew Howroyd_, Apr 26 2020
%Y Cf. A289719.
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Sep 02 2017
%E Terms a(21) and beyond from _Andrew Howroyd_, Apr 26 2020
|
