1,2

Alois P. Heinz, Table of n, a(n) for n = 1..200

F. Bergeron and F. Gascon, Counting Young tableaux of bounded height, J. Integer Sequences, Vol. 3 (2000), #00.1.7.

Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, and Jean-Marie Maillard, Stieltjes moment sequences for pattern-avoiding permutations, arXiv:2001.00393 [math.CO], 2020.

Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, and Jean-Marie Maillard, Stieltjes Moment Sequences for Pattern-Avoiding Permutations, Electron. J. Combin., Vol. 27, No. 4 (2020), p. 33.

Shalosh B. Ekhad, Nathaniel Shar, and Doron Zeilberger, The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r, arXiv:1504.02513 [math.CO], 2015.

Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.

Nathaniel Shar, Experimental methods in permutation patterns and bijective proof, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.

a(n) ~ 6075 * 7^(2*n + 49/2) / (32768 * n^24 * Pi^3). - Vaclav Kotesovec, Sep 10 2014

a:= proc(n) option remember; `if`(n<8, n!, ((-343035+429858*n

+238440*n^3+38958*n^4+634756*n^2+2940*n^5+84*n^6)*a(n-1)

-(1974*n^4+36336*n^3+213240*n^2+407840*n+82425)*(n-1)^2*a(n-2)

+2*(49875+42646*n+6458*n^2)*(n-1)^2*(n-2)^2*a(n-3)

-11025*(n-1)^2*(n-2)^2*(n-3)^2*a(n-4))/ ((n+6)^2*(n+10)^2*(n+12)^2))

end:

seq (a(n), n=1..30); # Alois P. Heinz, Sep 26 2012

h[l_] := With[{n = Length[l]}, Sum[i, {i, l}]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}] ]; g[n_, i_, l_] := If[n==0 || i==1, h[Join[l, Array[1&, n]]]^2, If[i<1, 0, Sum[g[n - i*j, i-1, Join[l, Array[i&, j]]], {j, 0, n/i}]]]; a[n_] := If[n <= 7, n!, g[n, 7, {}]]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz (A214015) *)

Cf. A052399 for T_6(n), A047890 for T_5(n), A047889 for T_4(n).

Column k=7 of A214015.

Sequence in context: A360384 A226439 A248840 * A230051 A067455 A033646

Adjacent sequences: A072128 A072129 A072130 * A072132 A072133 A072134

Jesse Carlsson (j.carlsson(AT)physics.unimelb.edu.au), Jun 25 2002

Typo in title corrected by Joel B. Lewis, Jul 16 2009

approved