A336184 a(n) = n^3 + (1/n) * Sum_{k=1..n-1} binomial(n,k) * k * a(k) * (n-k)^3.

1, 9, 53, 466, 5569, 82656, 1474045, 30664656, 729036801, 19499288680, 579487528861, 18943592776032, 675568129695601, 26099852672860344, 1085904530481561645, 48407032164910589056, 2301727955153266523521, 116286277045753464506568, 6220517619913795356269725

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

E.g.f.: -log(1 - exp(x) * x * (1 + 3*x + x^2)).

E.g.f.: -log(1 - Sum_{k>=1} k^3 * x^k / k!).

a(n) ~ (n-1)! / r^n, where r = 0.336491770414014560614859141224061461582454518... is the root of the equation exp(r)*r*(1 + 3*r + r^2) = 1. - Vaclav Kotesovec, Jul 11 2020

Mathematica

a[n_] := a[n] = n^3 + (1/n) Sum[Binomial[n, k] k a[k] (n - k)^3, {k, 1, n - 1}]; Table[a[n], {n, 1, 19}]
nmax = 19; CoefficientList[Series[-Log[1 - Exp[x] x (1 + 3 x + x^2)], {x, 0, nmax}], x] Range[0, nmax]! // Rest

Crossrefs

Cf. A000578, A279358, A300452, A305990, A308862, A336183.

Sequence in context: A003698 A001688 A144040 * A326606 A052108 A209453

Adjacent sequences: A336181 A336182 A336183 * A336185 A336186 A336187

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 10 2020

Status

approved