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Number of compositions of 2n into exactly 2n nonnegative parts with largest part n.
3

%I #8 Sep 20 2019 03:51:11

%S 1,1,18,195,1652,12825,96030,705341,5116200,36773397,262462010,

%T 1862790699,13160496684,92624149475,649794035142,4545979700445,

%U 31727803153232,220975193536845,1536191185018770,10661898343645847,73890140441316420,511405029708269529

%N Number of compositions of 2n into exactly 2n nonnegative parts with largest part n.

%H Alois P. Heinz, <a href="/A318161/b318161.txt">Table of n, a(n) for n = 0..1204</a>

%F a(n) = A180281(2n,n).

%F For n>0, a(n) = n - 2*n^2 + 2*n*binomial(3*n - 2, n). - _Vaclav Kotesovec_, Sep 20 2019

%e a(2) = 18: 0022, 0112, 0121, 0202, 0211, 0220, 1012, 1021, 1102, 1120, 1201, 1210, 2002, 2011, 2020, 2101, 2110, 2200.

%t Flatten[{1, Table[n - 2*n^2 + 2*n*Binomial[3*n - 2, n], {n, 1, 20}]}] (* _Vaclav Kotesovec_, Sep 20 2019 *)

%Y Bisection of A318160 (even part).

%Y Cf. A180281.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 19 2018