|
| |
|
|
A136556
|
|
Row 0 of square array A136555; a(n) = C(2^n - 1,n).
|
|
3
| |
|
|
1, 1, 3, 35, 1365, 169911, 67945521, 89356415775, 396861704798625, 6098989894499557055, 331001552386330913728641, 64483955378425999076128999167, 45677647585984911164223317311276545
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Number of n x n binary matrices without zero rows and with distinct rows up to permutation of rows, cf. A014070.
|
|
|
FORMULA
| a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(2^n,k).
a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*(2^n-1)^k. G.f.: Sum_{n>=0} ln(1+2^n*x)^n/((1+2^n*x)*n!).
G.f.: A(x) = Sum_{n>=0} (1 + 2^n*x)^-1 * log(1 + 2^n*x)^n / n!.
|
|
|
EXAMPLE
| G.f.: A(x) = 1 + x + 3*x^2 + 35*x^3 + 1365*x^4 + 169911*x^5 +...
A(x) = (1+x)^-1 + (1+2x)^-1*log(1+2x) + (1+4x)^-1*log(1+4x)^2/2! + (1+8x)^-1*log(1+8x)^3/3! +...
|
|
|
MATHEMATICA
| f[n_] := Binomial[2^n - 1, n]; Array[f, 12] (* RGWv *)
|
|
|
PROG
| (PARI) a(n)=binomial(2^n-1, n) (PARI) /* As coefficient of x^n in the g.f.: */ {a(n)=polcoeff(sum(i=0, n, (1+2^i*x+x*O(x^n))^-1*log(1+2^i*x+x*O(x^n))^i/i!), n)}
|
|
|
CROSSREFS
| Cf. A136555; A014070, A136505, A136506; A136557.
Cf. A066384.
Sequence in context: A062699 A012767 A136525 * A006098 A012499 A125530
Adjacent sequences: A136553 A136554 A136555 * A136557 A136558 A136559
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 07 2008; Paul Hanna and Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 15 2008
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 26 2008
|
| |
|
|
