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A341360
Diagonal elements of the array in A341359.
1
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).
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
KEYWORD
nonn
AUTHOR
Max Alekseyev, Feb 09 2021
STATUS
approved