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A225779
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Largest coefficient of (1 + x + ... + x^11)^n.
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5
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1, 1, 12, 108, 1156, 12435, 137292, 1528688, 17232084, 195170310, 2228154512, 25506741084, 293661065788, 3386455204288, 39222848622984, 454745042732160, 5290621952635476, 61590267941514516, 719050614048219912, 8397773337294253140, 98314091309732350656
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OFFSET
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0,3
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COMMENTS
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Generally, largest coefficient of (1 + x + ... + x^k)^n is asymptotic to (k+1)^n * sqrt(6/(k*(k+2)*Pi*n)).
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LINKS
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FORMULA
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a(n) ~ 12^n * sqrt(6/(143*Pi*n)).
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MAPLE
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P:= add(x^i, i=0..11):
seq(coeff(P^n, x, floor(11*n/2)), n=0..50); # Robert Israel, Jan 30 2017
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MATHEMATICA
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Flatten[{1, Table[Coefficient[Expand[Sum[x^j, {j, 0, 11}]^n], x^Floor[11*n/2]], {n, 1, 20}]}]
f[n_] := Max[CoefficientList[Sum[x^k, {k, 0, 11}]^n, x]]; Array[f, 20, 0] (* Robert G. Wilson v, Jan 29 2017 *)
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PROG
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(PARI) a(n) = vecmax(Vec(Pol(vector(12, k, 1))^n)); \\ Michel Marcus, Jan 29 2017
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CROSSREFS
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Cf. A001405, A002426, A005190, A005191, A018901, A025012, A025013, A025014, A025015, A201549, A201550.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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