

A246472


Number of orderpreserving (monotone) functions from the power set of 1 = {0} to the power set of n = {0, ..., n1}.


0



1, 3, 9, 30, 109, 418, 1650, 6604, 26589, 107274, 432934, 1746484, 7040626, 28362324, 114175812, 459344920, 1847008989, 7423262554, 29822432862, 119766845860, 480833598054, 1929896415484, 7744047734652, 31067665113640, 124613703290994, 499744683756868
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OFFSET

0,2


COMMENTS

This is the number of ways to choose a pair of elements (x,y) of P(n) so that x is a subset of y. This also gives the number of covariant functors from P(1) to P(n) viewed as categories.


LINKS

Table of n, a(n) for n=0..25.


FORMULA

a(n) = sum_{i=0..n} (binomial(n,i)*(1 + sum_{j=i+1..n} binomial(n,j)).
a(n) = 2^(2*n1) + 2^n  binomial(2*n, n)/2.  Vaclav Kotesovec, Aug 28 2014
n*(n4)*a(n) +2*(5*n^2+23*n15)*a(n1) +4*(8*n^241*n+45)*a(n2) 16*(2*n5)*(n3)*a(n3)=0.  R. J. Mathar, Jul 15 2017


MATHEMATICA

Sum[Binomial[#, i](1+ Sum[Binomial[#, j], {j, i+1, #}]), {i, 0, #}]& /@ Range[0, 20]


PROG

(PARI) a(n) = sum(i=0, n, binomial(n, i)*(1+ sum(j = i+1, n, binomial(n, j)))); \\ Michel Marcus, Aug 27 2014


CROSSREFS

Matches A129167 with offset 2 for the first four terms.
Sequence in context: A099783 A200074 A032125 * A091699 A129167 A151472
Adjacent sequences: A246469 A246470 A246471 * A246473 A246474 A246475


KEYWORD

nonn


AUTHOR

Jesse Han, Aug 27 2014


STATUS

approved



