0,3

Labeled posets where for all i,j,k in the set, do not have a<b<c. Labeled digraphs where every node has indegree 0 or outdegree 0.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19.

Index entries for sequences related to posets

Sum((-1)^k*C(n, k)*A047863(k), k=0..n).

a(n) = Sum_{k=0..n} binomial(n, k)*(2^k-1)^(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 04 2003

E.g.f. A(x) = Sum_{n>=0} exp((2^k-1)*x)*x^n/n!. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 27 2007

O.g.f.: Sum_{n>=0} x^n/(1 - (2^n - 1)*x)^(n+1) = Sum_{n>=0} a(n)*x^n. [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 15 2009]

(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp((2^k-1)*x)*x^k/k!), n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 27 2007

(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-(2^k-1)*x +x*O(x^n))^(k+1)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 15 2009]

Cf. A002031, A047863, A052332, A001833, A048194.

Row sums of A052296.

Cf. variants: A135753, A135754.

Sequence in context: A157451 A152112 A054420 this_sequence A002725 A097711 A114477

Adjacent sequences: A001828 A001829 A001830 this_sequence A001832 A001833 A001834

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms, formula and comments from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.

Last 4 terms corrected by Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 04 2003