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A216964 Triangle read by rows, arising in enumeration of permutations by cyclic valleys, cycles and fixed points. 1
1, 2, 6, 22, 2, 94, 26, 460, 244, 16, 2532, 2124, 384, 15420, 18536, 6092, 272, 102620, 166440, 83436, 10384, 739512, 1550864, 1082712, 247776, 7936, 5729192, 15040112, 13841928, 4864480, 441088, 47429896, 151960264, 177512632, 87003032, 14741984, 353792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See Ma and Chow (2012) for precise definition (see Corollary 5).

LINKS

Table of n, a(n) for n=1..37.

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

First column is A187251.

Sequence in context: A263486 A182544 A216120 * A187250 A129534 A216719

Adjacent sequences:  A216961 A216962 A216963 * A216965 A216966 A216967

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Sep 27 2012

EXTENSIONS

More terms from Michel Marcus, Feb 08 2013

STATUS

approved

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Last modified April 9 20:55 EDT 2020. Contains 333363 sequences. (Running on oeis4.)