A346380 Complement of A187430 in A000108.

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.

Links

Table of n, a(n) for n=0..30.

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

Cf. A000108, A055113, A111160, A187430.

Sequence in context: A183039 A192527 A227773 * A371552 A189737 A261567

Adjacent sequences: A346377 A346378 A346379 * A346381 A346382 A346383

Keyword

nonn

Author

F. Chapoton, Jul 14 2021

Status

approved