OFFSET
0,3
COMMENTS
Generally, largest coefficient of (1 + x + ... + x^k)^n is asymptotic to (k+1)^n * sqrt(6/(k*(k+2)*Pi*n)).
LINKS
Robert Israel, Table of n, a(n) for n = 0..927
FORMULA
a(n) ~ 12^n * sqrt(6/(143*Pi*n)).
MAPLE
P:= add(x^i, i=0..11):
seq(coeff(P^n, x, floor(11*n/2)), n=0..50); # Robert Israel, Jan 30 2017
MATHEMATICA
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 *)
PROG
(PARI) a(n) = vecmax(Vec(Pol(vector(12, k, 1))^n)); \\ Michel Marcus, Jan 29 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 09 2013
STATUS
approved