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%I #15 Aug 28 2022 04:23:45
%S 1,1,1,6,18,50,195,392,1652,2970,12825,22022,96030,160888,705341,
%T 1162800,5116200,8335338,36773397,59366450,262462010,420630210,
%U 1862790699,2967563040,13160496684,20861295000,92624149475,146203657992,649794035142,1021964428880
%N Number of compositions of n into exactly n nonnegative parts with largest part ceiling(n/2).
%H Alois P. Heinz, <a href="/A318160/b318160.txt">Table of n, a(n) for n = 0..2409</a>
%F a(n) = A180281(n,ceiling(n/2)).
%F a(n) = 3^(3*n/2 - 7/4 + (-1)^n/4) * sqrt(n/Pi) / 2^(n - 3/2). - _Vaclav Kotesovec_, Sep 21 2019
%e a(3) = 6: 012, 021, 102, 120, 201, 210.
%e a(4) = 18: 0022, 0112, 0121, 0202, 0211, 0220, 1012, 1021, 1102, 1120, 1201, 1210, 2002, 2011, 2020, 2101, 2110, 2200.
%e a(5) = 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.
%t b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, 0, Sum[b[n - j, i - 1, k], {j, 0, Min[n, k]}]]];
%t a[n_] := If[n == 0, 1, b[n, n, Ceiling[n/2]] - b[n, n, Ceiling[n/2] - 1]];
%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Aug 28 2022, after _Alois P. Heinz_ in A180281 *)
%Y Bisections give: A318161 (even part), A318162 (odd part).
%Y Cf. A180281.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Aug 19 2018
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