cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A186860 #18 Feb 20 2023 07:51:38
%S A186860 1,2,7,49,562,9132,207915,6296448,239972192,11427298486,661227186254,
%T A186860 45688884832738,3716852205228166,351101915633367990,
%U A186860 38275029480566516322,4750162039324230600200,666311679640315952033655,105085327413072323807645048
%N A186860 Largest coefficient of (1)(1+2x)(1+2x+3x^2)*...*(1+2x+3x^2+...+(n+1)*x^n).
%H A186860 Vaclav Kotesovec, <a href="/A186860/b186860.txt">Table of n, a(n) for n = 1..200</a>
%F A186860 Conjecture: a(n) ~ 3^(3/2) * sqrt(Pi) * n^(2*n + 1/2) / (2^(n-1) * exp(2*n)). - _Vaclav Kotesovec_, Jan 05 2023
%t A186860 f[n_] := Max@ CoefficientList[ Expand@ Product[ Sum[(i + 1)*x^i, {i, 0, j}], {j, n - 1}], x]; Array[f, 18]
%o A186860 (Sage)
%o A186860 def A186860(n):
%o A186860     p = prod(sum(i*x^(i-1) for i in (1..k)) for k in (1..n))
%o A186860     return Integer(max(p.coefficients())[0]) # _D. S. McNeil_, Feb 28 2011
%Y A186860 Cf. A000140, A186772.
%K A186860 easy,nonn
%O A186860 1,2
%A A186860 _Robert G. Wilson v_, Feb 27 2011