A001827 Related to graded partially ordered sets.

1, 4, 22, 166, 1726, 24814, 494902, 13729846, 531077086, 28697950174, 2170176736102, 230007989092006, 34211282155446286, 7149766552058591374, 2101690590380890192342, 869808621195903097079446, 507261036269544624540347326

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Corresponds to the numbers c(4,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. [Annotated scanned copy]
• D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19.
• Index entries for sequences related to posets

Crossrefs

Column k=4 of A361950.

Cf. A000684, A001828, A001829, A001830, A047863.

Formula

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

Extensions

More terms from Sean A. Irvine, Sep 24 2015