OFFSET
1,5
LINKS
C. Bean, M. Tannock, H. Ulfarsson, Pattern avoiding permutations and independent sets in graphs, arXiv:1512.08155 [math.CO], 2015, Theorem 3.5.
FORMULA
The bivariate g.f. G(x,y) satisfies G = 1+x*G+x*y*G^2/(1-y*(G-1)).
n*T(n,k) = Sum_{j=0..n-1} binomial(n,k-j)*binomial(n,j+1)*binomial(n-1+j,n-1).
EXAMPLE
1;
1, 1;
1, 3, 3;
1, 6, 14, 16;
1, 10, 40, 85, 105;
1, 15, 90, 295, 594, 771;
1, 21, 175, 805, 2331, 4529, 6083;
1, 28, 308, 1876, 7280, 19348, 36644, 50464;
1, 36, 504, 3906, 19404, 66780, 166608, 309537, 434493;
MATHEMATICA
T[n_, k_] := Binomial[n-1, k] HypergeometricPFQ[{-k, 2-n, n-1}, {2, n-k}, 1];
Table[T[n, k], {n, 1, 10}, {k, 0, n-1}] (* Jean-François Alcover, Sep 28 2019 *)
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Nov 20 2016
STATUS
approved