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%I #13 Jun 14 2013 05:22:15
%S 1,1,-2,1,-4,2,1,-6,8,-4,1,-8,18,-16,-4,1,-10,32,-44,12,-48,1,-12,50,
%T -96,72,-96,-336,1,-14,72,-180,216,-216,-480,-2928,1,-16,98,-304,500,
%U -544,-376,-4672,-28144,1,-18,128,-476,996,-1312,256,-5856,-45520,-298528
%N Triangle of numbers obtained by inverting infinite matrix defined in A059369, read from right to left.
%e Triangle starts
%e 1;
%e 1, -2;
%e 1, -4, 2;
%e 1, -6, 8, -4;
%e 1, -8, 18, -16, -4;
%e 1, -10, 32, -44, 12, -48;
%e 1, -12, 50, -96, 72, -96, -336;
%e 1, -14, 72, -180, 216, -216, -480, -2928;
%e 1, -16, 98, -304, 500, -544, -376, -4672, -28144;
%e 1, -18, 128, -476, 996, -1312, 256, -5856, -45520, -298528;
%e ... - _Joerg Arndt_, Apr 20 2013
%t nmax = 10; t[n_, k_] := t[n, k] = Sum[(m+1)!*t[n-m-1, k-1], {m, 0, n-k}]; t[n_, 1] = n!; t[n_, n_] = 1; tnk = Table[t[n, k], {n, 1, nmax}, {k, 1, nmax}]; Reverse /@ Inverse[tnk] // DeleteCases[#, 0, 2]& // Flatten (* _Jean-François Alcover_, Jun 14 2013 *)
%Y Cf. A059369, A059372, A059373.
%K sign,tabl,easy
%O 0,3
%A _N. J. A. Sloane_, Jan 28 2001
%E More terms from _Vladeta Jovovic_, Mar 05 2001
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