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A154420
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Maximal coefficient of MacMahon polynomial (cf. A060187) p(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; that is, a(n) = Max(coefficients(p(x,n))).
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2
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1, 1, 6, 23, 230, 1682, 23548, 259723, 4675014, 69413294, 1527092468, 28588019814, 743288515164, 16818059163492, 504541774904760, 13397724585164019, 455522635895576646, 13892023109165902550, 527896878148304296900
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OFFSET
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0,3
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COMMENTS
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Since the center is the maximum in the Pascal, Eulerian and MacMahon triangles, a(n)=MacMahon[n,Floor[n/2]]
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LINKS
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FORMULA
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MAPLE
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gf := proc(n, k) local f; f := (x, t) -> x*exp(t*x/k)/(1-x*exp(t*x));
series(f(x, t), t, n+2); ((1-x)/x)^(n+1)*k^n*n!*coeff(%, t, n):
collect(simplify(%), x) end:
seq(coeff(gf(n, 1), x, iquo(n, 2)), n=0..18); # Middle Eulerian numbers, A006551.
seq(coeff(gf(n, 2), x, iquo(n, 2)), n=0..18); # Middle midpoint Eulerian numbers.
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MATHEMATICA
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p[x_, n_] = 2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2];
Table[Max[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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