A166899 a(n) = Sum_{k=0..[n/2]} C(n-k,k)^4*n/(n-k), n>=1.

1, 3, 25, 111, 456, 2697, 15961, 86247, 495781, 3003738, 17946798, 107667969, 660458787, 4081397547, 25274724105, 157744019799, 991384251102, 6254115981009, 39613066988527, 252017709962526, 1608980424431755

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..501 [Offset shifted by Georg Fischer, Nov 20 2024]

Formula

Logarithmic derivative of A166898.

a(n) ~ 5^(3/4) * phi^(4*n+3) / (2^(5/2) * Pi^(3/2) * n^(3/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Nov 27 2017

Example

L.g.f.: L(x) = x + 3*x^2/2 + 25*x^3/3 + 111*x^4/4 + 456*x^5/5 + 2697*x^6/6 +...
exp(L(x)) = 1 + x + 2*x^2 + 10*x^3 + 38*x^4 + 137*x^5 + 646*x^6 + 3241*x^7 +...+ A166898(n)*x^n +...

Mathematica

Table[Sum[Binomial[n - k, k]^4 *n/(n - k), {k, 0, Floor[n/2]}], {n, 1, 50}] (* G. C. Greubel, May 27 2016 *)

Prog

(PARI) a(n)=sum(k=0, n\2, binomial(n-k, k)^4*n/(n-k))

Crossrefs

Cf. A166898, variants: A167539, A166895, A166897.

Sequence in context: A124245 A360788 A373682 * A201534 A059457 A165206

Adjacent sequences: A166896 A166897 A166898 * A166900 A166901 A166902

Keyword

nonn

Author

Paul D. Hanna, Nov 23 2009

Extensions

Offset changed to 1 by Georg Fischer, Nov 20 2024

Status

approved