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A060690 a(n) = C(2^n + n - 1, n). 20
1, 2, 10, 120, 3876, 376992, 119877472, 131254487936, 509850594887712, 7145544812472168960, 364974894538906616240640, 68409601066028072105113098240, 47312269462735023248040155132636160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of n X n (0,1) matrices modulo rows permutation (by symmetry this is the same as the number of (0,1) matrices modulo columns permutation), i.e. the number of equivalence classes where two matrices A and B are equivalent if one of them is the result of permuting the rows of the other. The total number of (0,1) matrices is in sequence A002416.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..59

FORMULA

a(n) = [x^n] 1/(1-x)^(2^n).

a(n) = (1/n!)*Sum((-1)^(n-k)*Stirling1(n, k)*2^(k*n), k=0..n). - Vladeta Jovovic, May 28 2004

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(2^n+n,k) = Sum_{k=0..n} Stirling1(n,k)*(2^n+n-1)^k. G.f.: Sum_{n>=0} (-ln(1-2^n*x))^n/n!. - Paul Hanna and Vladeta Jovovic, Jan 21 2008

G.f.: A(x) = Sum_{n>=0} [ -log(1 - 2^n*x)]^n / n!. More generally, Sum_{n>=0} [ -log(1 - q^n*x)]^n/n! = Sum_{n>=0} C(q^n+n-1,n)*x^n ; also Sum_{n>=0} log(1 + q^n*x)^n/n! = Sum_{n>=0} C(q^n,n)*x^n. - Paul D. Hanna, Dec 29 2007

MAPLE

with(combinat): for n from 1 to 20 do printf(`%d, `, binomial(2^n+n-1, n)) od:

MATHEMATICA

Table[Binomial[2^n+n-1, n], {n, 0, 20}] (* Harvey P. Dale, Apr 19 2012 *)

PROG

(PARI) a(n)=binomial(2^n+n-1, n)

(PARI) {a(n)=polcoeff(sum(k=0, n, (-log(1-2^k*x +x*O(x^n)))^k/k!), n)} - Paul D. Hanna, Dec 29 2007

(PARI) { for (n=0, 59, write("b060690.txt", n, " ", binomial(2^n + n - 1, n)); ) } [From Harry J. Smith, Jul 09 2009]

CROSSREFS

Cf. A002416, A060336, A088309, A132683, A132684.

Sequence in context: A110951 A172477 A120597 * A005617 A013038 A005321

Adjacent sequences:  A060687 A060688 A060689 * A060691 A060692 A060693

KEYWORD

nonn

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 19 2001

EXTENSIONS

More terms from James A. Sellers, Apr 20 2001

Edited by N. J. A. Sloane, Mar 17 2008

STATUS

approved

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Last modified October 25 14:15 EDT 2014. Contains 248544 sequences.