

A289428


Sum of factorialCatalan numbers over a certain family of decorations.


5




OFFSET

0,2


COMMENTS

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


LINKS

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


FORMULA

The following are conjectural (Cf. A145879):
Recurrence: a(n) = n*a(n1) + 2*Sum_{k = 1..n} a(k1)*a(nk) with a(0) = 1.
O.g.f. as a regular Cfraction: 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



KEYWORD

nonn,more


AUTHOR



STATUS

approved



