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A146900
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Symmetrical polynomial: t0(n,m)=If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[t0(n,m)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]/2].
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0
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1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 6, 9, 6, 1, 1, 11, 15, 15, 11, 1, 1, 9, 31, 30, 31, 9, 1, 1, 15, 43, 71, 71, 43, 15, 1, 1, 12, 42, 84, 105, 84, 42, 12, 1, 1, 19, 54, 126, 189, 189, 126, 54, 19, 1, 1, 15, 91, 180, 315, 378, 315, 180, 91, 15, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:{1, 2, 5, 16, 23, 54, 112, 260, 383, 778, 1582}.
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FORMULA
| t0(n,m)=If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[t0(n,m)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]/2]; t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {1}, {1, 1}, {1, 3, 1}, {1, 7, 7, 1}, {1, 6, 9, 6, 1}, {1, 11, 15, 15, 11, 1}, {1, 9, 31, 30, 31, 9, 1}, {1, 15, 43, 71, 71, 43, 15, 1}, {1, 12, 42, 84, 105, 84, 42, 12, 1}, {1, 19, 54, 126, 189, 189, 126, 54, 19, 1}, {1, 15, 91, 180, 315, 378, 315, 180, 91, 15, 1}
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MATHEMATICA
| Clear[t, p, x, n] t[n_, m_] = If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p[x_, n_] = If[n == 0, 1, (x + 1)^n + Sum[t[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]/(2)]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Sequence in context: A193387 A185982 A133800 * A132733 A082039 A176331
Adjacent sequences: A146897 A146898 A146899 * A146901 A146902 A146903
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2008
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