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

0,3

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

Table of n, a(n) for n=0..18.

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

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 *)

Crossrefs

Sequence in context: A100597 A352184 A022562 * A320954 A322725 A339832

Adjacent sequences: A341357 A341358 A341359 * A341361 A341362 A341363

Keyword

nonn

Author

Max Alekseyev, Feb 09 2021

Status

approved