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%I #14 Oct 14 2022 12:48:19
%S 1,1,0,1,0,0,1,0,1,0,1,0,2,0,0,1,0,3,2,1,0,1,0,4,6,6,0,0,1,0,5,12,21,
%T 10,1,0,1,0,6,20,52,60,22,0,0,1,0,7,30,105,204,183,42,1,0,1,0,8,42,
%U 186,520,820,546,86,0,0,1,0,9,56,301,1110,2605,3276,1641,170,1,0
%N Array read by antidiagonals: T(m,n) is the number of closed walks of length n on the complete graph on m nodes, m >= 1, n >= 0.
%F T(m,n) = ((m-1)^n + (m-1)(-1)^n)/m.
%F G.f.: T(m, n) = [z^n](1 - (m-2)z)/(1 - (m-2)z - (m-1)z^2).
%e Array begins:
%e m\n| 0 1 2 3 4 5 6 7 8 9 10
%e ---+------------------------------------------------------------
%e 1 | 1 0 0 0 0 0 0 0 0 0 0
%e 2 | 1 0 1 0 1 0 1 0 1 0 1
%e 3 | 1 0 2 2 6 10 22 42 86 170 342
%e 4 | 1 0 3 6 21 60 183 546 1641 4920 14763
%e 5 | 1 0 4 12 52 204 820 3276 13108 52428 209716
%e 6 | 1 0 5 20 105 520 2605 13020 65105 325520 1627605
%e 7 | 1 0 6 30 186 1110 6666 39990 239946 1439670 8638026
%e 8 | 1 0 7 42 301 2100 14707 102942 720601 5044200 35309407
%e 9 | 1 0 8 56 456 3640 29128 233016 1864136 14913080 119304648
%e 10 | 1 0 9 72 657 5904 53145 478296 4304673 38742048 348678441
%Y Rows are A078008, A054878, A109499, A109500, A109501.
%K nonn,easy,tabl
%O 1,13
%A _Mitch Harris_, Jun 30 2005
%E Corrected by _Franklin T. Adams-Watters_, Sep 18 2006
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