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A014070 a(n) = binomial(2^n, n). 46
1, 2, 6, 56, 1820, 201376, 74974368, 94525795200, 409663695276000, 6208116950265950720, 334265867498622145619456, 64832175068736596027448301568, 45811862025512780638750907861652480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of n X n (0,1) matrices with distinct rows modulo rows permutations. - Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 13 2003

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..60

FORMULA

G.f.: A(x) = Sum_{n>=0} log(1 + 2^n*x)^n / n!. - Paul D. Hanna, Dec 28 2007

From Vaclav Kotesovec, Jul 02 2016: (Start)

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

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

(End)

MAPLE

A014070:= n-> binomial(2^n, n); seq(A014070(n), n=0..20); # G. C. Greubel, Mar 14 2021

MATHEMATICA

Table[Binomial[2^n, n], {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2011 *)

PROG

(PARI) a(n)=binomial(2^n, n)

(PARI) /* G.f. A(x) as Sum of Series: */ a(n)=polcoeff(sum(k=0, n, log(1+2^k*x +x*O(x^n))^k/k!), n) \\ Paul D. Hanna, Dec 28 2007

(MAGMA) [Binomial(2^n, n): n in [0..25]]; // Vincenzo Librandi, Sep 13 2016

(Sage) [binomial(2^n, n) for n in (0..20)] # G. C. Greubel, Mar 14 2021

CROSSREFS

Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), this sequence (0,0), A136505 (0,1), A136506 (0,2), A060690 (1,-1), A132683 (1,0), A132684 (1,1), A132685 (2,0), A132686 (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).

Cf. A088229, A136393, A136555.

Sequence in context: A318001 A211933 A167010 * A320287 A198445 A248377

Adjacent sequences:  A014067 A014068 A014069 * A014071 A014072 A014073

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 21 03:51 EDT 2021. Contains 345354 sequences. (Running on oeis4.)