OFFSET
1,2
COMMENTS
See Ma and Chow (2012) for precise definition (see Corollary 5).
LINKS
Shi-Mei Ma and Chak-On Chow, Enumeration of permutations by number of cyclic peaks and cyclic valleys, arXiv preprint arXiv:1203.6264 [math.CO], 2012.
EXAMPLE
Triangle begins:
1
2
6
22, 2
94, 26
460, 244, 16
2532, 2124, 384
...
MATHEMATICA
rows = 12;
Reap[For[P = x*y; n = 1; Sow[{1}], n < rows, n++, P = (n*q + x*y)*P + 2*q*(1-q)*D[P, q] + 2*x*(1-q)*D[P, x] + (1-2*y+q*y)*D[P, y] // Simplify; Sow[CoefficientList[P /. {x -> 1, y -> 1}, q]]]][[2, 1]] // Flatten (* Jean-François Alcover, Sep 23 2018, from PARI *)
PROG
(PARI) tabf(m) = {P = x*y; for (n=1, m, M = subst(P, x, 1); M = subst(M, y, 1); for (d=0, poldegree(M, q), print1(polcoeff(M, d, q), ", "); ); print(""); P = (n*q+x*y)*P + 2*q*(1-q)*deriv(P, q)+ 2*x*(1-q)*deriv(P, x)+ (1-2*y+q*y)*deriv(P, y); ); } \\ Michel Marcus, Feb 08 2013
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Sep 27 2012
EXTENSIONS
More terms from Michel Marcus, Feb 08 2013
STATUS
approved