A001829 Related to graded partially ordered sets.

1, 6, 46, 450, 5650, 91866, 1957066, 55363650, 2109599650, 109773407466, 7894945079386, 792252362302770, 111671194813402930, 22202849561274787866, 6241728810901739517226, 2484011055161613143144610, 1400187830319472451472442690

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Corresponds to the numbers c(6,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=6 of A361950.

Cf. A000684, A001827, A001828, A001830, A047863.

Formula

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