A186860 Largest coefficient of (1)(1+2x)(1+2x+3x^2)*...*(1+2x+3x^2+...+(n+1)*x^n).

1, 2, 7, 49, 562, 9132, 207915, 6296448, 239972192, 11427298486, 661227186254, 45688884832738, 3716852205228166, 351101915633367990, 38275029480566516322, 4750162039324230600200, 666311679640315952033655, 105085327413072323807645048

Offset: 1

Author

Robert G. Wilson v, Feb 27 2011

Keywords

• easy
• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000140, A186772.

Programs

Mathematica

f[n_] := Max@ CoefficientList[ Expand@ Product[ Sum[(i + 1)*x^i, {i, 0, j}], {j, n - 1}], x]; Array[f, 18]

Sage

def A186860(n):
    p = prod(sum(i*x^(i-1) for i in (1..k)) for k in (1..n))
    return Integer(max(p.coefficients())[0]) # D. S. McNeil, Feb 28 2011

Formula

Conjecture: a(n) ~ 3^(3/2) * sqrt(Pi) * n^(2*n + 1/2) / (2^(n-1) * exp(2*n)). - Vaclav Kotesovec, Jan 05 2023