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A166897 a(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k), n>=1. 5
1, 3, 13, 39, 126, 477, 1765, 6495, 24709, 95128, 367368, 1431453, 5620343, 22170543, 87858813, 349708431, 1397003136, 5598513261, 22502171771, 90681323364, 366299212873, 1482827487650, 6014529069540, 24439715146941 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Logarithmic derivative of A166896.
a(n) ~ sqrt(15) * phi^(3*n + 2) / (6*Pi*n), 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 + 13*x^3/3 + 39*x^4/4 + 126*x^5/5 + 477*x^6/6 +...
exp(L(x)) = 1 + x + 2*x^2 + 6*x^3 + 16*x^4 + 45*x^5 + 142*x^6 + 459*x^7 +...+ A166896(n)*x^n/n +...
MATHEMATICA
Table[Sum[Binomial[n-k, k]^3 n/(n-k), {k, 0, Floor[n/2]}], {n, 30}] (* Harvey P. Dale, Mar 05 2013 *)
PROG
(PARI) a(n)=sum(k=0, n\2, binomial(n-k, k)^3*n/(n-k))
CROSSREFS
Cf. A166897, variants: A167539, A166895, A166899.
Sequence in context: A320661 A122504 A103277 * A167910 A147042 A018492
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 23 2009
STATUS
approved

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Last modified June 17 22:48 EDT 2024. Contains 373466 sequences. (Running on oeis4.)