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%I #18 Apr 27 2020 06:26:37
%S 1,2,7,31,141,631,2773,12013,51481,218791,923781,3879877,16224937,
%T 67603901,280816201,1163381401,4808643121,19835652871,81676217701,
%U 335780006101,1378465288201,5651707681621,23145088600921,94684453367401,386971244197201,1580132580471901
%N a(n) = (n/2)*binomial(2*n, n) + 1.
%H Andrew Howroyd, <a href="/A289719/b289719.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 37, tables 4.1 and 4.2
%F a(n) = 1 + A002457(n-1).
%p seq(1+n/2*binomial(2*n,n),n=0..20) ;
%t Table[(n/2) Binomial[2 n, n] + 1, {n, 0, 20}] (* _Michael De Vlieger_, Sep 05 2017 *)
%o (GAP)
%o A289719:=List([0..10^2], n->(n/2)*Binomial(2*n,n)+1); # _Muniru A Asiru_, Sep 03 2017
%o (PARI) a(n) = {n*binomial(2*n, n)/2 + 1} \\ _Andrew Howroyd_, Apr 26 2020
%Y Cf. A002457, A289720.
%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