A378079 Number of series-reduced noncrossing trees with n edges.

1, 1, 0, 4, 5, 33, 91, 408, 1485, 6195, 24838, 103752, 432796, 1834140, 7815900, 33591376, 145197017, 631281591, 2757917260, 12102728740, 53321334381, 235768155073, 1045889996047, 4653534540816, 20761857325000, 92862669150004, 416316199107096, 1870414803490240

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Formula

G.f.: 1/(1 - g(x)) - g(x)^2 where g(x) is the g.f. of A030980.

Example

The a(3) = 4 trees are:
    o---o    o---o    o   o    o   o
    | \        / |    | /        \ |
    o   o    o   o    o---o    o---o

Prog

(PARI) seq(n)={my(g=serreverse(x/(1/(1-x)^2 - 2*x) + O(x*x^n))); Vec(1/(1 - g) - g^2)}

Crossrefs

Cf. A000014, A001764, A030980, A378078.

Sequence in context: A215614 A013468 A376536 * A244333 A041907 A228662

Adjacent sequences: A378076 A378077 A378078 * A378080 A378081 A378082

Keyword

nonn

Author

Andrew Howroyd, Nov 21 2024

Status

approved