Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Sep 02 2024 21:57:00
%S 1,1,2,3,5,8,14,24,43,78,144,269,509,971,1868,3618,7049,13805,27162,
%T 53661,106405,211697,422458,845386,1696017,3410522,6873060,13878721,
%U 28077439,56900936,115501012,234807488,478032437,974507543,1989123814
%N Diagonal sums of the number triangle associated to A086617.
%C The triangle associated to A086617 is given by T(n,k)=if(k<=n, sum{j=0..n-k, C(n-k,j)C(k,j)C(j)},0). A050253(n)=A108296(n+2)-A108296(n).
%F G.f.: (1-x^2-sqrt(1-2*x^2-4*x^3-3*x^4))/(2*x^3*(1-x^2)).
%F a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2*k} binomial(n-2*k, j)*binomial(k, j) * A000108(j).
%F Conjecture: (n+3)*a(n) +(-n-2)*a(n-1) +2*(-n-1)*a(n-2) +2*(-n+3)*a(n-3) +(n+1)*a(n-4) +3*(n-2)*a(n-5)=0. - _R. J. Mathar_, Nov 16 2012
%K easy,nonn
%O 0,3
%A _Paul Barry_, May 31 2005