A005477 a(n) = 2^(n-1)*(2^n - 1)*Product_{j=1..n-1} (2^j + 1).

0, 1, 18, 420, 16200, 1138320, 152681760, 40012315200, 20727639504000, 21349793828563200, 43852643645542617600, 179883715700853141120000, 1474687052822610564537600000, 24170122236238340825650936320000, 792151597973733707815459821941760000, 51919200227802645600849976559054284800000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..75

Crossrefs

Cf. A081845.

Programs

Magma

[n le 1 select n else 2^(n-1)*(2^n -1)*(&*[2^j+1: j in [1..n-1]]): n in [0..25]]; // G. C. Greubel, Nov 25 2022

Maple

f := i->2^(i-1)*(2^i-1)*product( '2^j+1','j'=1..i-1);

Mathematica

Table[2^(n-1) (2^n-1)Product[2^j+1,{j,n-1}],{n,0,20}] (* Harvey P. Dale, Feb 02 2022 *)
Table[2^(n-2)*(2^n-1)*QPochhammer[-1,2,n], {n,0,30}] (* G. C. Greubel, Nov 25 2022 *)

SageMath

def A005477(n): return 2^(n-2)*(2^n-1)*product(2^j+1 for j in range(n))
[A005477(n) for n in range(30)] # G. C. Greubel, Nov 25 2022

Formula

a(n) = 2^(n-2)*(2^n - 1)*QPochhammer(n, -1, 2). - G. C. Greubel, Nov 25 2022

a(n) ~ c * 2^((n^2+3*n-4)/2), where c = Product_{k>=0} (1 + 1/2^k) = A081845. - Amiram Eldar, Aug 18 2025

Extensions

a(0) prepended by G. C. Greubel, Nov 25 2022