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%I #3 Jul 15 2012 09:53:49
%S 1,1,1,5,6,1,93,115,23,1,5993,7436,1518,76,1,1272089,1578757,322762,
%T 16330,237,1,857402029,1064110290,217560951,11012540,160571,722,1,
%U 1792650585525,2224835452407,454875884137,23025275075,335768223,1512581
%N Matrix inverse of the MacMahon numbers A060187 by way of recursive calculation.
%C Row sums are:
%C {1, 2, 12, 232, 15024, 3190176, 2150247104, 4495724480128, 28750797892487936,
%C 557764883306639383040, 32668026499694843494640640,...}
%F m=2;
%F A(n,k)= (m*n - m*k + 1)A(n - 1, k - 1) + (m*k - (m - 1))A(n - 1, k)
%e {1},
%e {1, 1},
%e {5, 6, 1},
%e {93, 115, 23, 1},
%e {5993, 7436, 1518, 76, 1},
%e {1272089, 1578757, 322762, 16330, 237, 1},
%e {857402029, 1064110290, 217560951, 11012540, 160571, 722, 1},
%e {1792650585525, 2224835452407, 454875884137, 23025275075, 335768223, 1512581, 2179, 1},
%e {11464255554367057, 14228139328931096, 2908996087466828, 147249943814184, 2147290464886, 9673492136, 13945196, 6552, 1},
%e {222406320165016449457, 276025608122908733321, 56434463826320585284, 2856645864675796564, 41657391444153086, 187665608020478, 270538484020, 127141156, 19673, 1},
%e {13026233415367869864109781, 16166689855580307839632286, 3305339964838291288943901, 167312402773377971746920, 2439853795947184617546, 10991486289326969076, 15845312257310658, 7446608913000, 1152338433, 59038, 1}
%t Clear[t, M, a, m] m = 2; A[n_, 1] := 1
%t A[n_, n_] := 1
%t A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]
%t a = Table[A[n, k], {n, 12}, {k, n}]
%t M[n_] := Table[If[k <= m, (-1)^(m + k)*a[[m, k]], 0], {k, 1, n}, {m, 1, n}]
%t Table[Table[Inverse[M[12]][[m, n]], {m, 1, n}], {n, 1, 11}]
%t Flatten[%]
%Y A060187, A055325, A154921,
%K nonn,uned
%O 1,4
%A _Roger L. Bagula_ and Mats Granvik, Dec 06 2009
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