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Search: id:A141905
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| A141905 |
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A skew trinomial summed triangular sequence of coefficients: t(n,m)=Sum[n!/((n - m - k)!*m!*k!), {k, 0, m}]. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 9, 6, 1, 1, 16, 24, 8, 1, 1, 25, 70, 40, 10, 1, 1, 36, 165, 160, 60, 12, 1, 1, 49, 336, 525, 280, 84, 14, 1, 1, 64, 616, 1456, 1120, 448, 112, 16, 1, 1, 81, 1044, 3528, 3906, 2016, 672, 144, 18, 1, 1, 100, 1665, 7680, 11970, 8064, 3360, 960, 180, 20, 1
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 2, 6, 17, 50, 147, 435, 1290, 3834, 11411, 34001}.
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FORMULA
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t(n,m)=Sum[n!/((n - m - k)!*m!*k!), {k, 0, m}].
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EXAMPLE
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{1},
{1, 1},
{1, 4, 1},
{1, 9, 6, 1},
{1, 16, 24, 8, 1},
{1, 25, 70, 40, 10, 1},
{1, 36, 165, 160, 60, 12, 1},
{1, 49, 336, 525, 280, 84, 14, 1},
{1, 64, 616, 1456, 1120, 448, 112, 16, 1},
{1, 81, 1044, 3528, 3906, 2016, 672, 144, 18, 1},
{1, 100, 1665, 7680, 11970, 8064, 3360, 960, 180, 20, 1}
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MATHEMATICA
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Clear[t, n, m]; t[n_, m_] = Sum[n!/((n - m - k)!*m!*k!), {k, 0, m}]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A055107 A128137 A136100 this_sequence A114188 A110511 A082950
Adjacent sequences: A141902 A141903 A141904 this_sequence A141906 A141907 A141908
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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 14 2008
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