%I #14 Jan 01 2018 04:58:14
%S 1,1,0,1,5,6,3,13,42,55,55,162,413,591,810,2001,4451,6900,11091,24795,
%T 51030,84337,147253,309666,610695,1058041,1928646,3903175,7528741,
%U 13480380,25126093,49640405,94739568,173440389,326974495,636424008
%N Diagonal sums of a Krawtchouk triangle.
%C Diagonal sums of A099037.
%H G. C. Greubel, <a href="/A099038/b099038.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*Sum_{i=0..n} (-1)^i*C(k, i) * C(n-2k, k-i).
%F Conjecture: n*a(n) -n*a(n-1) +n*a(n-2) +3*(-n+1)*a(n-3) +(-5*n+13)*a(n-4) +(n-3)*a(n-5)=0. - _R. J. Mathar_, Dec 21 2014
%t Table[Sum[Binomial[n - k, k]*Sum[(-1)^i*Binomial[k, i]*Binomial[n - 2*k, k - i], {i, 0, n}], {k, 0, Floor[n/2]}], {n,0,50}] (* _G. C. Greubel_, Dec 31 2017 *)
%o (PARI) for(n=0,30, print1(sum(k=0,floor(n/2), binomial(n-k,k)*sum(i=0,n,(-1)^i*binomial(k,i)*binomial(n-2*k,k-i))), ", ")) \\ _G. C. Greubel_, Dec 31 2017
%Y Cf. A077948.
%K easy,nonn
%O 0,5
%A _Paul Barry_, Sep 23 2004