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A346380
Complement of A187430 in A000108.
0
0, 0, 1, 0, 3, 3, 18, 39, 157, 459, 1668, 5503, 19638, 68325, 245144, 876438, 3177651, 11549939, 42307920, 155555733, 574881920, 2132231076, 7938771624, 29651189637, 111086480106, 417305224917, 1571633677078, 5932720163529, 22443721850064, 85075094996719, 323086777251300
OFFSET
0,5
COMMENTS
Related to the decomposition of A000108 as the sum of A055113 and A111160.
FORMULA
G.f. y(x) satisfies x y^4 + 2 x^2 y^2 + x^3 + 3 x y^2 + y^3 - x y = 0.
PROG
(Sage)
N = 30
x = (PowerSeriesRing(QQ, 'x').0).O(N + 1)
f = (x*(1-x^2)^2/(1+x^3)^2).reverse()
g = sum(catalan_number(n)*x**n for n in range(N + 1)).O(N + 1)
list(x*g-f)
CROSSREFS
KEYWORD
nonn
AUTHOR
F. Chapoton, Jul 14 2021
STATUS
approved