A086905 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(k,floor(k/2)).
1, 0, 2, 1, 5, 5, 15, 20, 50, 76, 176, 286, 638, 1078, 2354, 4081, 8789, 15521, 33099, 59279, 125477, 227239, 478193, 873885, 1830271, 3370029, 7030571, 13027729, 27088871, 50469889, 104647631, 195892564, 405187826, 761615284, 1571990936
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- H. Prodinger, The Kernel Method: a collection of examples, Séminaire Lotharingien de Combinatoire, B50f (2004), 19 pp.
Programs
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Mathematica
Table[Sum[(-1)^(n-k)*Binomial[k,Floor[k/2]],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Mar 02 2014 *) -
PARI
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(k,k\2)); \\ Michel Marcus, Dec 04 2016
Formula
G.f.: (sqrt((1+2*x)/(1-2*x))-1)/2/x/(1+x).
a(n) ~ 2^(n+3/2) / (3*sqrt(Pi*n)) * (1 - 2/(3*n)+ 3*(-1)^n/(4*n)). - Vaclav Kotesovec, Mar 02 2014
Comments