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A171859 a(n) = Bell(n) - Sum_{j=0..n-1} Bell(j), where the Bell numbers are given in A000110. 1
1, 0, 0, 1, 6, 28, 127, 598, 2984, 15851, 89532, 536152, 3392609, 22609852, 158220300, 1159380201, 8873605258, 70778190768, 587125257319, 5055713850058, 45114387675316, 416535887361323, 3973511993495144, 39112086371684844 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of partitions of the set {1,2,...,n} in which n is neither a singleton nor is in a block of consecutive integers. Example: a(4)=6 because we have 14-23, 13-24, 134-2, 124-3, 1-24-3, and 14-2-3. Note that if from the other partitions of {1,2,3,4}, namely 1234, 1-234, 12-34, 1-2-34, 123-4, 1-23-4, 12-3-4, 13-2-4, 1-2-3-4, we delete the blocks containing 4, then we are left with empty, 1, 12, 1-2, 123, 1-23, 12-3, 13-2, 1-2-3, i.e., all the partitions of the sets: empty, {1}, {1,2}, and {1,2,3}.

a(n) = A000110(n) - A005001(n).

LINKS

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

FORMULA

G.f.: G(0)*(1-x-x^2)/(1-x^2) + x/(1-x^2) where G(k) = 1 - x*(1-k*x)/(1 - x - x^2 - (1-2*x-x^2+2*x^3+x^4)/(1 - x - x^2 + (1-k*x)*(k*x+x-1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 10 2013

MAPLE

with(combinat): seq(bell(n)-add(bell(j), j = 0 .. n-1), n = 0 .. 23);

CROSSREFS

Cf. A000110, A005001.

Sequence in context: A002693 A289779 A117423 * A084778 A287807 A155588

Adjacent sequences:  A171856 A171857 A171858 * A171860 A171861 A171862

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 01 2010

STATUS

approved

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Last modified February 17 17:52 EST 2019. Contains 320222 sequences. (Running on oeis4.)