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%I #2 Oct 12 2012 14:54:51
%S 1,1,3,1,10,1,1,25,19,3,1,56,126,56,1,1,119,594,614,109,3,1,246,2367,
%T 4852,2367,246,1,1,501,8565,31273,31203,8607,487,3,1,1012,29188,
%U 176524,312310,176524,29188,1012,1,1,2035,95644,910468,2620582,2620834,910300
%N A linear combination of A008292 and A130595: t(n,m)=2*A008292(n,m)- A130595(n,m).
%C Row sums are:
%C {1, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600}.
%F t(n,m)=2*A008292(n,m)- A130595(n,m).
%e {1},
%e {1, 3},
%e {1, 10, 1},
%e {1, 25, 19, 3},
%e {1, 56, 126, 56, 1},
%e {1, 119, 594, 614, 109, 3},
%e {1, 246, 2367, 4852, 2367, 246, 1},
%e {1, 501, 8565, 31273, 31203, 8607, 487, 3},
%e {1, 1012, 29188, 176524, 312310, 176524, 29188, 1012, 1},
%e {1, 2035, 95644, 910468, 2620582, 2620834, 910300, 95716, 2017, 3}
%t A[n_, 1] := 1 A[n_, n_] := 1 A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + k A[n - 1, k]; Table[Table[2*A[n, k] - (-1)^(k + 1)*Binomial[n - 1, k - 1], {k, 1, n}], {n, 1, 10}]; Flatten[%]
%Y Cf. A008292 and A130595.
%K nonn,uned
%O 1,3
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 14 2008
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