A101346 a(n) = binomial(2^n, n-1).

1, 4, 28, 560, 35960, 7624512, 5423611200, 13161885792000, 110859231254749120, 3293259778311548232704, 349928324708588104171703296, 134575849279352109587517966790656, 189165427620415586720308268784807487488, 979739920960712963224129514007339757999308800

Offset: 1

Author

Jorge Coveiro, Dec 25 2004

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A014070. - Paul D. Hanna, Jun 21 2009

Programs

Maple

seq(binomial(2^n,n-1),n=1..20);

Mathematica

Table[Binomial[2^n,n-1], {n,1,15}] (* Vaclav Kotesovec, Jul 02 2016 *)

PARI

a(n)=binomial(2^n,n-1) \\ Paul D. Hanna, Jun 21 2009

PARI

a(n)=polcoeff(x*sum(k=0,n,2^k*log(1+2^k*x+x*O(x^n))^k/k!),n) \\ Paul D. Hanna, Jun 21 2009

Formula

G.f.: A(x) = x*Sum_{n>=0} 2^n*log(1+2^n*x)^n/n!. - Paul D. Hanna, Jun 21 2009

a(n) ~ 2^(n*(n-1)) / (n-1)!. - Vaclav Kotesovec, Jul 02 2016

Extensions

Terms a(13) and beyond from Andrew Howroyd, Feb 12 2020