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%I #39 Jun 20 2022 04:17:17
%S 1,1,12,108,1156,12435,137292,1528688,17232084,195170310,2228154512,
%T 25506741084,293661065788,3386455204288,39222848622984,
%U 454745042732160,5290621952635476,61590267941514516,719050614048219912,8397773337294253140,98314091309732350656
%N Largest coefficient of (1 + x + ... + x^11)^n.
%C Generally, largest coefficient of (1 + x + ... + x^k)^n is asymptotic to (k+1)^n * sqrt(6/(k*(k+2)*Pi*n)).
%H Robert Israel, <a href="/A225779/b225779.txt">Table of n, a(n) for n = 0..927</a>
%F a(n) ~ 12^n * sqrt(6/(143*Pi*n)).
%p P:= add(x^i,i=0..11):
%p seq(coeff(P^n,x,floor(11*n/2)),n=0..50); # _Robert Israel_, Jan 30 2017
%t Flatten[{1, Table[Coefficient[Expand[Sum[x^j, {j,0,11}]^n], x^Floor[11*n/2]], {n,1,20}]}]
%t f[n_] := Max[CoefficientList[Sum[x^k, {k, 0, 11}]^n, x]]; Array[f, 20, 0] (* _Robert G. Wilson v_, Jan 29 2017 *)
%o (PARI) a(n) = vecmax(Vec(Pol(vector(12,k,1))^n)); \\ _Michel Marcus_, Jan 29 2017
%Y Cf. A001405, A002426, A005190, A005191, A018901, A025012, A025013, A025014, A025015, A201549, A201550.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Aug 09 2013
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