A185970 a(n) = 2^((n^2-n-2)/2)*(n+2)!

1, 3, 24, 480, 23040, 2580480, 660602880, 380507258880, 487049291366400, 1371530804487782400, 8426685262772935065600, 112176034218033311593267200, 3216311253099451110002157158400, 197610163390430276198532535812096000, 25901159335910477161894056533963046912000

Offset

0,2

Comments

a(n) is the determinant of the symmetric matrix (if(j<=floor((i+j)/2), 2^k*(k+1), 2^n*(n+1)))_{0<=i,j<=n}.

Links

G. C. Greubel, Table of n, a(n) for n = 0..77

Formula

a(n) = 2^binomial(n,2)*A001710(n+2).

a(n) = 2^binomial(n+1,2)*Product_{k=0..n} (k+2)/2} = Product_{k=0..n} 2^k*(k+2)/2.

Example

a(3)=280 since det[1, 1, 1, 1; 1, 4, 4, 4; 1, 4, 12, 12; 1, 4, 12, 32]=280.

Mathematica

Table[2^((n^2 - n - 2)/2)*(n + 2)!, {n, 0, 50}] (* G. C. Greubel, Jul 23 2017 *)

Prog

(PARI) for(n=0, 50, print1(2^((n^2 - n - 2)/2)*(n + 2)!, ", ")) \\ G. C. Greubel, Jul 23 2017

Crossrefs

Cf. A001787.

Sequence in context: A002832 A233151 A236466 * A279165 A336577 A194157

Adjacent sequences: A185967 A185968 A185969 * A185971 A185972 A185973

Keyword

nonn,easy

Author

Paul Barry, Feb 16 2011

Status

approved