A001828 Related to graded partially ordered sets.

1, 5, 33, 287, 3309, 50975, 1058493, 29885567, 1156711869, 61815727295, 4589058616413, 475576073939807, 69061902766811229, 14093318360697120095, 4049931601653596366013, 1641314561238334948886207, 939097032426474389539281789

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Corresponds to the numbers c(5,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=5 of A361950.

Cf. A000684, A001827, A001829, A001830, A047863.

Formula

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

Extensions

More terms from Sean A. Irvine, Sep 24 2015