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A094762 a(n) = Bell(n+1) - 2^n + 1 + n, where Bell(i) is the i-th Bell number A000110(i). 0
1, 2, 4, 11, 41, 177, 820, 4020, 20900, 115473, 677557, 4211561, 27640354, 190891144, 1382942176, 10480109395, 82864804285, 682076675105, 5832741942932, 51724157711104, 474869815108196, 4506715736350193, 44152005850890065, 445958869286416705 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the solution to the following combinatorial problem. Given a set S of n labeled elements, find the number of all subsets of S (2^n) plus the number of partitions of any subset T of S into parts which are not all of size 1 nor of size |T|. This implies that a(n) = 2^n + Sum_{m=3..n} (Bell(m)-2) = Bell(n+1) - 2^n + 1 + n, using the standard recurrence for the Bell numbers (Comtet, Eq. (4a)). - N. J. A. Sloane, Nov 26 2013

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 210.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

Also a(n) = 2^n + Sum_{m=3..n} binomial(n,m)*(Bell(m)-2).

MAPLE

with(combinat); [seq(bell(n+1)-2^n+n+1, n=0..30)];

CROSSREFS

Cf. A000110, A144646.

Sequence in context: A012948 A013182 A013170 * A099934 A067353 A105996

Adjacent sequences:  A094759 A094760 A094761 * A094763 A094764 A094765

KEYWORD

nonn

AUTHOR

Jean-Yves Tallet and N. J. A. Sloane, Jan 24 2009

STATUS

approved

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Last modified March 30 20:18 EDT 2017. Contains 284302 sequences.