OFFSET
0,3
COMMENTS
This is a convolution of A091156 with itself (see the Pudwell link below).
LINKS
Alois P. Heinz, Rows n = 0..120, flattened
A. M. Baxter, Refining enumeration schemes to count according to permutation statistics, arXiv preprint arXiv:1401.0337 [math.CO], 2014.
M. Bukata, R. Kulwicki, N. Lewandowski, L. Pudwell, J. Roth, and T. Wheeland, Distributions of Statistics over Pattern-Avoiding Permutations, arXiv preprint arXiv:1812.07112 [math.CO], 2018.
L. Pudwell, On the distribution of peaks (and other statistics), 2018.
FORMULA
G.f.: G(q,z) = - (-2z^3q^2+4z^3q-2z^3-2z^2q+2z^2-1+sqrt(-4z^2q+4z^2-4z+1))/(2z(zq-z+1)^2). (See the Pudwell link above.)
EXAMPLE
Triangle begins:
1;
1;
2;
3, 2;
4, 10;
5, 32, 5;
6, 84, 42;
7, 198, 210, 14;
8, 438, 816, 168;
9, 932, 2727, 1152, 42;
10, 1936, 8250, 5940, 660;
...
MATHEMATICA
m = maxExponent = 15;
G = -(-2 z^3 q^2 + 4z^3 q - 2z^3 - 2z^2 q + 2z^2 - 1 + Sqrt[-4z^2 q + 4z^2 - 4z + 1])/(2z (z q - z + 1)^2);
CoefficientList[# + O[q]^m, q]& /@ CoefficientList[G + O[z]^m, z]// Flatten (* Jean-François Alcover, Aug 06 2018 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jan 31 2014
EXTENSIONS
More terms from Alois P. Heinz, Apr 26 2018
STATUS
approved