A289428 Sum of factorial-Catalan numbers over a certain family of decorations.

1, 3, 18, 144, 1368, 14688, 173664, 2226528, 30647808

Offset

0,2

Comments

The precise definition involves the use of certain symbols akin to the peace symbol.

Links

Table of n, a(n) for n=0..8.

Vincent Pilaud, V. Pons, Permutrees, arXiv preprint arXiv:1606.09643 [math.CO], 2016.

Formula

From Peter Bala, Dec 25 2019: (Start)

The following are conjectural (Cf. A145879):

Recurrence: a(n) = n*a(n-1) + 2*Sum_{k = 1..n} a(k-1)*a(n-k) with a(0) = 1.

O.g.f. as a regular C-fraction: 1/(1 - 3*x/(1 - 3*x/(1 - 4*x/(1 - 4*x/(1 - 5*x/(1 - 5*x/(1 - ... ))))))). Cf. A111537.

exp( Sum_{n >= 1} a(n)*(2*x)^n/n ) = 1 + 6*x + 54*x^2 + 636*x^3 + ... appears to have integer coefficients. (End)

Crossrefs

Cf. A289427, A289429, A289430, A289431, A000142, A111537, A145879.

Sequence in context: A259904 A107708 A224992 * A123308 A177383 A074525

Adjacent sequences: A289425 A289426 A289427 * A289429 A289430 A289431

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 06 2017

Status

approved