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A153737
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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).
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2, 5040, 5040, 2, 80636, 2, 2, 362878, 362878, 2, 2, 363024, 6531548, 363024, 2, 2, 363206, 39553592, 39553592, 363206, 2, 2, 363428, 79849438, 797577464, 79849438, 363428, 2, 2, 363694, 128156058, 6098501046, 6098501046, 128156058, 363694, 2, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are (2*(n + 5)!) except for n=1:
{2, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600,
174356582400, 2615348736000}.
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FORMULA
| A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1).
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EXAMPLE
| {2},
{5040, 5040},
{2, 80636, 2},
{2, 362878, 362878, 2},
{2, 363024, 6531548, 363024, 2},
{2, 363206, 39553592, 39553592, 363206, 2},
{2, 363428, 79849438, 797577464, 79849438, 363428, 2},
{2, 363694, 128156058, 6098501046, 6098501046, 128156058, 363694, 2},
{2, 364008, 185214520, 18683169432, 136619086476, 18683169432, 185214520, 364008, 2},
{2, 364374, 251770836, 42192786508, 1265229446280, 1265229446280, 42192786508, 251770836, 364374, 2}
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MATHEMATICA
| Clear[A]; A[2, 1] := A[2, 2] = 7!;
A[3, 2] = 2*8! - 4; A[4, 2] = A[4, 3] = 9! - 2;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 4)*(n + 3)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 10}, {k, n}];
Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 10}]; |Q Table[Apply[Plus, a[[n]]]/(2*(n + 5)!), {n, 1, 10}];
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CROSSREFS
| Sequence in context: A067668 A195002 A203756 * A078933 A064029 A057645
Adjacent sequences: A153734 A153735 A153736 * A153738 A153739 A153740
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 31 2008
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