OFFSET
1,5
COMMENTS
Is this A094503 after removal of the top row? - R. J. Mathar, Aug 13 2008
LINKS
Chak-On Chow and Wai Chee Shiu, Counting Simsun Permutations by Descents, Ann. Comb. 15, 625-635 (2011). See p. 627.
Ming-Jian Ding and Bao-Xuan Zhu, Some results related to Hurwitz stability of combinatorial polynomials, Advances in Applied Mathematics, Volume 152, (2024), 102591. See p. 35.
R. P. Stanley, Flag f-vectors and the cd-index, Math. Zeitschrift 216 (1994), 483-499.
S. Sundaram, Plethysm, Partitions with an Even Number of Blocks and Euler Numbers, in "Formal Power Series and Algebraic Combinatorics 1994," DIMACS Series in Discrete Mathematics and Theoretical Computer Science 24, AMS (1996).
FORMULA
T(n, k) = (k+1)*T(n-1, k) + (n-2k+1)*T(n-1, k-1);
Row g.f.: T(n, t) = Sum_{k=0..floor(n/2)} T(n, k)*t^k,
T(n, t) = ((n-1)*t + 1)*T(n-1, t) + t*(1-2t)*T(n-1, t)'.
E.g.f.: Sum_{n>=1} T(n, t)*x^n/n! = (2t-1)*(sec(x*sqrt(2t-1)/2)/(sqrt(2t-1) - tan(x*sqrt(2t-1)/2)))^2.
EXAMPLE
Triangle begins
1;
1, 1;
1, 4;
1, 11, 4;
1, 26, 34;
1, 57, 180, 34;
...
MATHEMATICA
Table[SeriesCoefficient[(2t-1)*(Sec[x*Sqrt[2t-1]/2]/(Sqrt[2t-1]- Tan[x*Sqrt[2t-1]/2]))^2, {x, 0, n}, {t, 0, k}]n!, {n, 11}, {k, 0, Floor[n/2]}]//Flatten (* Stefano Spezia, Aug 09 2023 *)
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Chak-On Chow (cchow(AT)alum.mit.edu), Jan 28 2006
EXTENSIONS
Corrected and extended by Vladeta Jovovic, Jan 30 2006
STATUS
approved