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Search: id:A141678
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| A141678 |
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Symmetrical triangle of coefficients based on invert transform of A0001906: a(n) = Sum[k*a(n - k), {k, 1, n}] ( Invert transform); t(n,m)=a(n-m+1)*a(m+1). |
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+0
1
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| 1, 3, 3, 8, 9, 8, 21, 24, 24, 21, 55, 63, 64, 63, 55, 144, 165, 168, 168, 165, 144, 377, 432, 440, 441, 440, 432, 377, 987, 1131, 1152, 1155, 1155, 1152, 1131, 987, 2584, 2961, 3016, 3024, 3025, 3024, 3016, 2961, 2584, 6765, 7752, 7896, 7917, 7920, 7920, 7917
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:
{1, 6, 25, 90, 300, 954, 2939, 8850, 26195, 76500, 221016}.
Notice that the interior of the triangle are relatively "flat" : smaller
variation than in most symmetrical triangles of this type.
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FORMULA
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a(n) = Sum[k*a(n - k), {k, 1, n}]; t(n,m)=a(n-m+1)*a(m+1).
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EXAMPLE
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{1},
{3, 3},
{8, 9, 8},
{21, 24, 24, 21},
{55, 63, 64, 63, 55},
{144, 165, 168, 168, 165, 144},
{377, 432, 440, 441, 440, 432, 377},
{987, 1131, 1152, 1155, 1155, 1152, 1131, 987},
{2584, 2961, 3016, 3024, 3025, 3024, 3016, 2961, 2584},
{6765, 7752, 7896, 7917, 7920, 7920, 7917, 7896, 7752, 6765},
{17711, 20295, 20672, 20727, 20735, 20736, 20735, 20727, 20672, 20295, 17711}
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MATHEMATICA
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Clear[a, n]; a[0] = 1; a[n_] := a[n] = Sum[k*a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]; Table[Table[a[n - m + 1]*a[m + 1], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Cf. A001906.
Sequence in context: A094966 A095068 A021299 this_sequence A135477 A092549 A022663
Adjacent sequences: A141675 A141676 A141677 this_sequence A141679 A141680 A141681
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 07 2008
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