

A213048


Number of preferential arrangements of n labeled elements with repetitions allowed.


1



1, 1, 5, 31, 229, 1981, 19775, 224589, 2864901, 40591255, 632760105, 10765616885, 198543617119, 3945765358653, 84070841065937, 1911864488674531, 46222718892288645, 1183919151676806177, 32025836905529003471, 912372909851608715945, 27304698509111141688969
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OFFSET

0,3


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250


FORMULA

a(n) = Sum_{k=1..n} C(n+k1,k)*a(nk) for n>0, a(0) = 1.
a(n) = Sum_c(n) C(n+k11,k1) C(nk1+k21,k2) C(nk1k2+k31,k3) ..., where Sum_c(n) denotes the sum over all compositions (ordered partitions) of n = k1 + k2 + ... .
a(n) ~ c * n! * n^(log(2)) / (log(2))^n, where c = 0.9387523255426859866752735339706007723805611... .  Vaclav Kotesovec, May 03 2015


EXAMPLE

For n=2 the a(2) = 5 solutions are (1,2), (12), (21), (11), (22).


MAPLE

a:= proc(n) option remember;
`if`(n=0, 1, add(binomial(n+k1, k)*a(nk), k=1..n))
end:
seq(a(n), n=0..25);


CROSSREFS

Cf. A000670.
Sequence in context: A001910 A052773 A062147 * A069321 A211179 A177797
Adjacent sequences: A213045 A213046 A213047 * A213049 A213050 A213051


KEYWORD

nonn


AUTHOR

Thomas Wieder, Jun 03 2012


STATUS

approved



