A166895 a(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k), n>=1.

1, 3, 7, 39, 366, 5697, 194881, 16288695, 2430565261, 564615230758, 257227244037248, 319346787227133873, 832952161388710135215, 3382434539389226013260403, 22966972221673234523620345857

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..50

Formula

Logarithmic derivative of A166894.

Limit_{n->oo} a(n)^(1/n^2) = (1/r - 1)^((1 - r)^2/(3 - 4*r)) = 1.436094496902535711953511352318447104797138641971237143543..., where r = A323777 = 0.220676041323740696312822269998050167187681031027574... is the root of the equation (1 - 2*r)^(3 - 4*r) = (1 - r)^(2*(1 - r))*r^(1 - 2*r). - Vaclav Kotesovec, Nov 20 2024

Example

L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 39*x^4/4 + 366*x^5/5 + 5697*x^6/6 +...
exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 14*x^4 + 89*x^5 + 1050*x^6 +...+ A166894(n)*x^n +...

Mathematica

Table[Sum[Binomial[n - k, k]^(n - k) *n/(n - k), {k, 0, Floor[n/2]}], {n, 1, 25}] (* G. C. Greubel, May 27 2016 *)

Prog

(PARI) a(n)=sum(k=0, n\2, binomial(n-k, k)^(n-k)*n/(n-k))

Crossrefs

Cf. A166894, A209428.

Sequence in context: A074582 A105621 A181081 * A368627 A018998 A018941

Adjacent sequences: A166892 A166893 A166894 * A166896 A166897 A166898

Keyword

nonn

Author

Paul D. Hanna, Nov 23 2009

Status

approved