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Search: id:A140874
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| A140874 |
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Triangular sequence of second integer differential of the binomial/ Pascal's triangle: t(n,m)=Binomial(n,m+2)-2(Binomial(n,m+1)+Binomial(n,m). |
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+0
1
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| -4, -4, -8, -3, -12, -13, -1, -15, -25, -19, 2, -16, -40, -44, -26, 6, -14, -56, -84, -70, -34, 11, -8, -70, -140, -154, -104, -43, 17, 3, -78, -210, -294, -258, -147, -53, 24, 20, -75, -288, -504, -552, -405, -200, -64
(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:
{-4, -12, -28, -60, -124, -252, -508, -1020, -2044};
First two are empty.
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REFERENCES
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*
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FORMULA
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t(n,m)=Binomial(n,m+2)-2(Binomial(n,m+1)+Binomial(n,m).
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EXAMPLE
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{-4},
{-4, -8},
{-3, -12, -13},
{-1, -15, -25, -19},
{2, -16, -40, -44, -26},
{6, -14, -56, -84, -70, -34},
{11, -8, -70, -140, -154, -104, -43},
{17, 3, -78, -210, -294, -258, -147, -53},
{24, 20, -75, -288, -504, -552, -405, -200, -64}
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MATHEMATICA
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Clear[T, D2, x, a, n, m] T[n_, m_] := Binomial[n, m] D2[n_, m_] := If[m + 2 <= n, T[n, m + 2] - 2*T[n, m + 1] - T[n, m], {} ]; a = Table[Flatten[Table[D2[n, m], {m, 0, n}]], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Cf. A007318.
Adjacent sequences: A140871 A140872 A140873 this_sequence A140875 A140876 A140877
Sequence in context: A067736 A091671 A137797 this_sequence A021227 A040013 A117973
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 21 2008
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