A001830 Related to graded partially ordered sets. (Formerly M4439 N1877)

1, 7, 61, 661, 8953, 152917, 3334921, 94354981, 3528929353, 177999003157, 12340001650921, 1194005625114661, 162936187792764073, 31536761103831315157, 8677703806537883683081, 3395880602480076153665701, 1889190751946097573211698313

Offset

0,2

Comments

Corresponds to the numbers c(7,n) in the Klarner paper. - Sean A. Irvine, Sep 24 2015

References

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

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

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

Links

John Cerkan, Table of n, a(n) for n = 0..112

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

Index entries for sequences related to posets

Formula

a(n) = Sum_{p+q+r+s+t+u+v=n} (n!/p!q!r!s!t!u!v!) 2^(pq+qr+rs+st+tu+uv) where (p,q,r,s,t,u,v) is any nonnegative composition of n. - Sean A. Irvine, Sep 24 2015

Crossrefs

Column k=7 of A361950.

Cf. A000684, A001827, A001828, A001829, A047863.

Sequence in context: A049402 A218498 A261687 * A213326 A261901 A368324

Adjacent sequences: A001827 A001828 A001829 * A001831 A001832 A001833

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Sep 24 2015

Status

approved