A001830 Related to graded partially ordered sets.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

References

• 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.
• 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

Crossrefs

Column k=7 of A361950.

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

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

Extensions

More terms from Sean A. Irvine, Sep 24 2015