A134173 a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2^k,n).

1, 3, 8, 68, 2106, 223776, 80532200, 98945392200, 421225839051260, 6310402120912239968, 337401124757628967733136, 65171905481441631827737564000, 45944096973025484590366745753166436

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..59

Formula

G.f.: Sum_{n>=0} log(1+(2^n+1)*x)^n/n!.

From Vaclav Kotesovec, Jul 02 2016: (Start)

a(n) ~ binomial(2^n,n).

a(n) ~ 2^(n^2) / n!.

a(n) ~ 2^(n^2 - 1/2) * exp(n) / (sqrt(Pi) * n^(n+1/2)).

(End)

Maple

a:=proc(n) options operator, arrow: sum(binomial(n, k)*binomial(2^k, n), k=0..n) end proc: seq(a(n), n=0..13); # Emeric Deutsch, Jan 27 2008

Mathematica

Table[Sum[Binomial[n, k]*Binomial[2^k, n], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)

Prog

(PARI) for(n=0, 25, print1(sum(k=0, n, binomial(n, k)*binomial(2^k, n)), ", ")) \\ G. C. Greubel, Mar 21 2017

Crossrefs

Sequence in context: A224230 A053740 A363312 * A095051 A362990 A092372

Adjacent sequences: A134170 A134171 A134172 * A134174 A134175 A134176

Keyword

easy,nonn

Author

Paul D. Hanna and Vladeta Jovovic, Jan 13 2008

Extensions

More terms from Emeric Deutsch, Jan 27 2008

Status

approved