OFFSET
0,3
COMMENTS
It is uncertain if the initial term should be 0 or 1. Both make sense. I have changed the data line to start with 1, in agreement with Riordan (1954). - N. J. A. Sloane, Jun 28 2015
See Riordan 1954 page 21 equation (24). - Michael Somos, Aug 26 2015
REFERENCES
R. P. Stanley, Enumerative Combinatorics I, Example 4.7.17.
LINKS
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy] See Table 1.
EXAMPLE
Triangle begins:
1,
1,3,
1,6,5,
1,9,18,6,
1,12,42,44,9,
1,15,75,145,95,13,
1,18,117,336,420,192,20,
1,21,168,644,1225,1085,371,31,
1,24,228,1096,2834,3880,2588,696,49,
1,27,297,1719,5652,10656,11097,5823,1278,78,
1,30,375,2540,10165,24626,35045,29380,12535,2310,125,
... (from N. J. A. Sloane, Jun 28 2015)
Sum_{n, k} T(n, k) u^n t^k = 1 + (1 + 3*t)*u + (1 + 6*t + 5*t^2)*u^2 + ...
MATHEMATICA
max = 11; f[x_, y_] := 1 + y*(1 + 3*x - 4*x^2*y - 3*x^2*y^2 - 3*x^3*y^2 + 4*x^4*y^3)/((1 - y - 2*x*y - x*y^2 + x^3*y^3)*(1 - x*y)); se = Series[f[x, y], {x, 0, max}, {y, 0, max}]; coes = CoefficientList[se, {x, y}] ; t[n_, k_] := coes[[k, n]]; Flatten[ Table[t[n, k], {n, 1, max}, {k, 1, n}]](* Jean-François Alcover, Oct 24 2011 *)
CROSSREFS
KEYWORD
AUTHOR
Vladeta Jovovic, Jun 18 2001
EXTENSIONS
Edited by N. J. A. Sloane, Jun 28 2015
STATUS
approved