OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..floor(k/2)} binomial(n-k+j, j).
a(n) = Sum_{k=0..floor(n/2)} binomial(n - k + floor(k/2) + 1, 1 + floor(k/2))*(1 + floor(k/2))/(n-k+1). - G. C. Greubel, Jul 24 2022
MAPLE
A099577 := proc(n)
local a, k ;
a := 0 ;
for k from 0 to floor(n/2) do
a := a+add(binomial(n-k+j, j), j=0..floor(k/2)) ;
end do:
a ;
end proc:
seq(A099577(n), n=0..50); # R. J. Mathar, Nov 28 2014
MATHEMATICA
Table[Sum[Binomial[n-k+Floor[k/2]+1, 1+Floor[k/2]]*(1+Floor[k/2])/(n-k+1), {k, 0, Floor[n/2]}], {n, 0, 40}] (* G. C. Greubel, Jul 24 2022 *)
PROG
(Magma) [(&+[Binomial(n-k+Floor(k/2)+1, 1+Floor(k/2))*(1+Floor(k/2))/(n-k+1): k in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, Jul 24 2022
(SageMath) [sum( binomial(n-k+(k//2)+1, 1+(k//2))*(1+(k//2))/(n-k+1) for k in (0..(n//2)) ) for n in (0..40)] # G. C. Greubel, Jul 24 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 23 2004
STATUS
approved