A011266 a(n) = 2^(n*(n-1)/2)*n!.

1, 1, 4, 48, 1536, 122880, 23592960, 10569646080, 10823317585920, 24936923717959680, 127677049435953561600, 1438154284846580917862400, 35344079704389572637386342400, 1882001556099335963795547960115200, 215842994465920643015783804449692057600

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Let A = the sum of the n-th powers of the first 2^{n-1} terms of A001969, and similarly let B = the sum of the n-th powers of the first 2^{n-1} terms of A000069. Then a(n) = |A-B|. - Jeffrey Shallit, Nov 29 2019

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..77
• Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8.

Crossrefs

Main diagonal of A046860.

Cf. A000069, A001969.

Programs

Maple

a:= n-> 2^(n*(n-1)/2)*n!:
seq(a(n), n=0..15);  # Alois P. Heinz, Apr 21 2020

Mathematica

Table[2^((n(n-1))/2) n!,{n,0,20}] (* Harvey P. Dale, Dec 16 2012 *)

PARI

a(n) = n! << binomial(n,2); \\ Kevin Ryde, Mar 10 2022

Formula

From Mehdi Naima, Mar 09 2022: (Start)

a(n) = a(n-1)*n*2^(n-1), a(0) = 1.

G.f. satisfies A(x) = 1 + x * (x * A(2*x))'. (End)