A289428 Sum of factorial-Catalan numbers over a certain family of decorations.
1, 3, 18, 144, 1368, 14688, 173664, 2226528, 30647808
Offset: 0
Links
- 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)
Comments