A059370 Triangle of numbers obtained by inverting infinite matrix defined in A059369, read from right to left.
1, 1, -2, 1, -4, 2, 1, -6, 8, -4, 1, -8, 18, -16, -4, 1, -10, 32, -44, 12, -48, 1, -12, 50, -96, 72, -96, -336, 1, -14, 72, -180, 216, -216, -480, -2928, 1, -16, 98, -304, 500, -544, -376, -4672, -28144, 1, -18, 128, -476, 996, -1312, 256, -5856, -45520, -298528
Offset: 0
Examples
Triangle starts 1; 1, -2; 1, -4, 2; 1, -6, 8, -4; 1, -8, 18, -16, -4; 1, -10, 32, -44, 12, -48; 1, -12, 50, -96, 72, -96, -336; 1, -14, 72, -180, 216, -216, -480, -2928; 1, -16, 98, -304, 500, -544, -376, -4672, -28144; 1, -18, 128, -476, 996, -1312, 256, -5856, -45520, -298528; ... - _Joerg Arndt_, Apr 20 2013
Programs
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Mathematica
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 *)
Extensions
More terms from Vladeta Jovovic, Mar 05 2001