A383569 -id:A383569 - cp's OEIS frontend

A383568 Expansion of 1/sqrt((1-x^5)^2 - 4*x^2).

1, 0, 2, 0, 6, 1, 20, 6, 70, 30, 253, 140, 936, 630, 3522, 2773, 13430, 12032, 51770, 51690, 201389, 220470, 789546, 935330, 3116416, 3951949, 12373910, 16645398, 49389050, 69938416, 198048409, 293296470, 797461358, 1228136090, 3222960100, 5136602753

Offset: 0

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Seiichi Manyama, Apr 30 2025

nonn

Number of lattice paths from (0,0) to (n,n) using steps (2,0),(0,2),(5,5).
Diagonal of the rational function 1 / (1 - x^2 - y^2 - x^5*y^5).
Diagonal of the rational function 1 / ((1-x^2*y)*(1-x^3*y^4) - y).

R. A. Sulanke, Moments of generalized Motzkin paths, J. Integer Sequences, Vol. 3 (2000), #00.1.

Main diagonal of A383567.

Cf. A002426, A053442, A383569.

my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x^5)^2-4*x^2))

cp's OEIS Frontend

A383568 Expansion of 1/sqrt((1-x^5)^2 - 4*x^2).

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