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%I #2 Mar 30 2012 17:34:29
%S 2,5040,5040,2,80636,2,2,362878,362878,2,2,363024,6531548,363024,2,2,
%T 363206,39553592,39553592,363206,2,2,363428,79849438,797577464,
%U 79849438,363428,2,2,363694,128156058,6098501046,6098501046,128156058,363694,2,2
%N A recursive triangular sequence with row sums (2*(n + 5)!): A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1).
%C Row sums are (2*(n + 5)!) except for n=1:
%C {2, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600,
%C 174356582400, 2615348736000}.
%F A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1).
%e {2},
%e {5040, 5040},
%e {2, 80636, 2},
%e {2, 362878, 362878, 2},
%e {2, 363024, 6531548, 363024, 2},
%e {2, 363206, 39553592, 39553592, 363206, 2},
%e {2, 363428, 79849438, 797577464, 79849438, 363428, 2},
%e {2, 363694, 128156058, 6098501046, 6098501046, 128156058, 363694, 2},
%e {2, 364008, 185214520, 18683169432, 136619086476, 18683169432, 185214520, 364008, 2},
%e {2, 364374, 251770836, 42192786508, 1265229446280, 1265229446280, 42192786508, 251770836, 364374, 2}
%t Clear[A]; A[2, 1] := A[2, 2] = 7!;
%t A[3, 2] = 2*8! - 4; A[4, 2] = A[4, 3] = 9! - 2;
%t A[n_, 1] := 2; A[n_, n_] := 2;
%t A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 4)*(n + 3)*A[n - 2, k - 1];
%t a = Table[A[n, k], {n, 10}, {k, n}];
%t Flatten[a]
%t Table[Apply[Plus, a[[n]]], {n, 1, 10}];|Q Table[Apply[Plus, a[[n]]]/(2*(n + 5)!), {n, 1, 10}];
%K nonn,tabl
%O 1,1
%A _Roger L. Bagula_, Dec 31 2008
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