Jean-Yves Tallet - cp's OEIS frontend

User: Jean-Yves Tallet

Jean-Yves Tallet has authored 2 sequences.

A144646 a(n) = Bell(n) - 2^n + n.

0, 0, 0, 0, 3, 25, 145, 756, 3892, 20644, 114961, 676533, 4209513, 27636258, 190882952, 1382925792, 10480076627, 82864738749, 682076544033, 5832741680788, 51724157186816, 474869814059620, 4506715734253041, 44152005846695761, 445958869278028097

Offset: 0

Jean-Yves Tallet and N. J. A. Sloane, Jan 26 2009

nonn

Number of partitions of an n-set having more than one block of size > 1. - Peter Luschny, Apr 10 2011

			a(5) = 25 = card({25|134, 35|124, 125|34, 345|12, 45|123, 235|14, 15|234, 145|23, 135|24, 245|13, 25|4|13, 35|4|12, 45|3|12, 5|24|13, 5|12|34, 1|35|24, 35|2|14, 25|3|14, 5|14|23, 1|45|23, 15|4|23, 45|2|13, 15|3|24, 15|2|34, 1|25|34}). - _Peter Luschny_, Apr 10 2011

Amiram Eldar, Table of n, a(n) for n = 0..576

Cf. A000110, A094782.

[Bell(n) -2^n +n: n in [0..30]]; // G. C. Greubel, Oct 12 2023

Table[BellB[n] - 2^n + n, {n, 0, 24}] (* Amiram Eldar, Nov 23 2019 *)

[bell_number(n) - 2^n +n for n in range(31)] # G. C. Greubel, Oct 12 2023

A094762 a(n) = Bell(n+1) - 2^n + 1 + n, where Bell(i) is the i-th Bell number A000110(i).

Original entry on oeis.org

1, 2, 4, 11, 41, 177, 820, 4020, 20900, 115473, 677557, 4211561, 27640354, 190891144, 1382942176, 10480109395, 82864804285, 682076675105, 5832741942932, 51724157711104, 474869815108196, 4506715736350193, 44152005850890065, 445958869286416705

Offset: 0

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

nonn

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

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

Cf. A000110, A144646.

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

Table[BellB[n+1]-2^n+n+1,{n,0,30}] (* Harvey P. Dale, Apr 24 2018 *)

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

cp's OEIS Frontend

User: Jean-Yves Tallet

A144646 a(n) = Bell(n) - 2^n + n.

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