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 #12 Feb 12 2021 11:38:49
%S 1,1,2,5,14,50,194,1319,8834,117869,1269734,560616089,510535634,
%T 750085374614,2035030321602194,223759362505832069,764885974089796574,
%U 2887808734792025240864461034,716116205417604827135407034
%N Diagonal elements of the array in A341359.
%C a(n) plays a crucial role in the formula for the generating function for the n-th row of A341359. Essentially the terms A341359(n,k) for k >= n equals the halved coefficient of x^(k-n+1) in sqrt((1-(4*a(n)+1)*x)/(1-x)).
%C The sequence is not monotone. For example, a(11) > a(12).
%H T. Amdeberhan et al. <a href="https://mathoverflow.net/q/380482">Sequences generated by sum & product of terms (with rotating indices): combinatorial?</a>, 2021.
%t T[m_, 0] := 1; T[m_, n_] := T[m, n] = Sum[T[m, k] * T[m, Mod[n - 1 - k + m, n]], {k, 0, n - 1}]; Table[T[n, n], {n, 0, 18}] (* _Amiram Eldar_, Feb 09 2021 *)
%K nonn
%O 0,3
%A _Max Alekseyev_, Feb 09 2021