A158817 a(n) = (binomial(2^n, 2^(n-1)) - binomial(2^(n-1), 2^(n-2)))/2^n.

1, 8, 800, 18783360, 28634752192836096, 187118328452563147377366903401859072, 22533823529098462258163079522899558155141642796614195116180863201125539840

Offset: 2

Author

Tanya Khovanova and Leonid Makar-Limanov, Mar 27 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..11
• Gyula O. H. Katona and Leonid Makar-Limanov, A problem for abelian groups, Asian-Eur. J. Math. 1 (2008), no. 2, 237--241. (Reviewer: Thomas Britz) 20K01 (05B40 94B65).

Crossrefs

Cf. A069954.

Programs

Mathematica

Table[(Binomial[2^n, 2^(n-1)] -Binomial[2^(n-1), 2^(n-2)])/2^n, {n, 2, 12}]

Sage

[( binomial(2^n, 2^(n-1)) - binomial(2^(n-1), 2^(n-2)) )/2^n for n in (2..12)] # G. C. Greubel, Dec 22 2021

Formula

a(n) = ( binomial(2^n, 2^(n-1)) - binomial(2^(n-1), 2^(n-2)) )/2^n.