A341360 Diagonal elements of the array in A341359.

1, 1, 2, 5, 14, 50, 194, 1319, 8834, 117869, 1269734, 560616089, 510535634, 750085374614, 2035030321602194, 223759362505832069, 764885974089796574, 2887808734792025240864461034, 716116205417604827135407034

Offset: 0

Author

Max Alekseyev, Feb 09 2021

Keywords

• nonn

Comments

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)).

The sequence is not monotone. For example, a(11) > a(12).

Links

• T. Amdeberhan et al. Sequences generated by sum & product of terms (with rotating indices): combinatorial?, 2021.

Programs

Mathematica

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 *)