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Search: id:A139158
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| A139158 |
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Hermite polynomial H(x,n) (A060821) interpolation as a triangular sequence of coefficients: Even-> 2*H(x,n); Odd ->H(x,n)+H(x,n+1). |
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+0
23
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| 2, 1, 2, 0, 4, -2, 2, 4, -4, 0, 8, -2, -12, 4, 8, 0, -24, 0, 16, 12, -12, -48, 8, 16, 24, 0, -96, 0, 32, 12, 120, -48, -160, 16, 32, 0, 240, 0, -320, 0, 64
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums:
{2, 3, 4, 4, 4, -2, -8, -24, -40, -28, -16}.
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FORMULA
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Even m-> p(x,m)=2*H(x,n); Odd m ->p(x,m)=H(x,n)+H(x,n+1).
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EXAMPLE
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{2},
{1, 2},
{0, 4},
{-2, 2, 4},
{-4, 0, 8},
{-2, -12, 4, 8},
{0, -24, 0, 16},
{12, -12, -48, 8, 16},
{24, 0, -96, 0, 32},
{12, 120, -48, -160, 16, 32},
{0, 240, 0, -320, 0, 64}.
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MATHEMATICA
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Clear[p, x] p[x, 0] = 2*HermiteH[0, x]; p[x, 1] = HermiteH[0, x] + HermiteH[1, x]; p[x, 2] = 2*HermiteH[1, x]; p[x_, m_] := p[x, m] = If[Mod[m, 2] == 0, 2*HermiteH[Floor[m/2], x], HermiteH[ Floor[m/2], x] + HermiteH[Floor[m/2 + 1], x]]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}]
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CROSSREFS
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Cf. A060821.
Sequence in context: A080966 A023895 A070963 this_sequence A055135 A121310 A092419
Adjacent sequences: A139155 A139156 A139157 this_sequence A139159 A139160 A139161
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KEYWORD
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nonn,uned,tabf
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 05 2008
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