A225779 Largest coefficient of (1 + x + ... + x^11)^n.

1, 1, 12, 108, 1156, 12435, 137292, 1528688, 17232084, 195170310, 2228154512, 25506741084, 293661065788, 3386455204288, 39222848622984, 454745042732160, 5290621952635476, 61590267941514516, 719050614048219912, 8397773337294253140, 98314091309732350656

Offset: 0

Author

Vaclav Kotesovec, Aug 09 2013

Keywords

• nonn

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
• Index entries for sequences of k-nomial coefficients

Crossrefs

Row 12 of A077042.

Programs

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 *)

PARI

a(n) = vecmax(Vec(Pol(vector(12,k,1))^n)); \\ Michel Marcus, Jan 29 2017

Formula

a(n) ~ 12^n * sqrt(6/(143*Pi*n)).