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Search: id:A153738
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| A153738 |
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Adjusted recursive triangular sequence with row sums 2*(n+5)!/6!: 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, 7, 7, 1, 110, 1, 1, 503, 503, 1, 1, 576, 8926, 576, 1, 1, 667, 54772, 54772, 667, 1, 1, 778, 118799, 1091404, 118799, 778, 1, 1, 911, 207621, 8440107, 8440107, 207621, 911, 1, 1, 1068, 329900, 27180372, 187139238, 27180372, 329900, 1068, 1, 1, 1251
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are:
{2, 14, 112, 1008, 10080, 110880, 1330560, 17297280, 242161920, 3632428800,...}.
The division by 6! and changing the first element gives a nicer looking result.
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FORMULA
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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
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{2},
{7, 7},
{1, 110, 1},
{1, 503, 503, 1},
{1, 576, 8926, 576, 1},
{1, 667, 54772, 54772, 667, 1},
{1, 778, 118799, 1091404, 118799, 778, 1},
{1, 911, 207621, 8440107, 8440107, 207621, 911, 1},
{1, 1068, 329900, 27180372, 187139238, 27180372, 329900, 1068, 1},
{1, 1251, 496770, 65297294, 1750419084, 1750419084, 65297294, 496770, 1251, 1}
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MATHEMATICA
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Clear[A] A[1, 1] = 2*6!/720; A[2, 1] := A[2, 2] = 7!/720;
A[3, 2] = (2*8! - 2*6!)/720; A[4, 2] = A[4, 3] = ( 9! - 6!)/720;
A[n_, 1] := 6!/720; A[n_, n_] := 6!/720;
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}];
Table[Apply[Plus, 720*a[[n]]]/(2*(n + 5)!), {n, 1, 10}];
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CROSSREFS
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Sequence in context: A155541 A021787 A011052 this_sequence A159790 A016639 A138341
Adjacent sequences: A153735 A153736 A153737 this_sequence A153739 A153740 A153741
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 31 2008
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