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A318162 Number of compositions of 2n-1 into exactly 2n-1 nonnegative parts with largest part n.

%I A318162 #10 Sep 20 2019 03:32:47
%S A318162 1,6,50,392,2970,22022,160888,1162800,8335338,59366450,420630210,
%T A318162 2967563040,20861295000,146203657992,1021964428880,7127260128736,
%U A318162 49606676100234,344658278690250,2390849931605590,16561583202364200,114577083158683530,791757148201073670
%N A318162 Number of compositions of 2n-1 into exactly 2n-1 nonnegative parts with largest part n.
%H A318162 Alois P. Heinz, <a href="/A318162/b318162.txt">Table of n, a(n) for n = 1..1205</a>
%F A318162 a(n) = A180281(2n-1,n).
%F A318162 For n>1, a(n) = 2*(2*n - 1) * binomial(3*n - 4, n-2). - _Vaclav Kotesovec_, Sep 20 2019
%e A318162 a(1) = 1: 1.
%e A318162 a(2) = 6: 012, 021, 102, 120, 201, 210.
%e A318162 a(3) = 50: 00023, 00032, 00113, 00131, 00203, 00230, 00302, 00311, 00320, 01013, 01031, 01103, 01130, 01301, 01310, 02003, 02030, 02300, 03002, 03011, 03020, 03101, 03110, 03200, 10013, 10031, 10103, 10130, 10301, 10310, 11003, 11030, 11300, 13001, 13010, 13100, 20003, 20030, 20300, 23000, 30002, 30011, 30020, 30101, 30110, 30200, 31001, 31010, 31100, 32000.
%p A318162 a:= proc(n) option remember; (2*n-1)*`if`(n<3, n,
%p A318162       3*(3*n-4)*(3*n-5)*a(n-1)/(2*(n-1)*(2*n-3)^2))
%p A318162     end:
%p A318162 seq(a(n), n=1..30);
%t A318162 Flatten[{1, Table[2*(2*n - 1)*Binomial[3*n - 4, n-2], {n, 2, 20}]}] (* _Vaclav Kotesovec_, Sep 20 2019 *)
%Y A318162 Bisection of A318160 (odd part).
%Y A318162 Cf. A180281.
%K A318162 nonn
%O A318162 1,2
%A A318162 _Alois P. Heinz_, Aug 19 2018