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A048742 n! - n-th Bell number. 3
0, 0, 0, 1, 9, 68, 517, 4163, 36180, 341733, 3512825, 39238230, 474788003, 6199376363, 86987391878, 1306291409455, 20912309745853, 355604563226196, 6401691628921841, 121639267666626943, 2432850284018404628, 51090467301893283249, 1123996221061869232677 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of permutations of [n] which have at least one cycle that has at least one inversion when written with its smallest element in the first position. Example: a(4)=9 because we have (1)(243), (1432), (142)(3), (132)(4), (1342), (1423), (1243), (143)(2) and (1324). - Emeric Deutsch, Apr 29 2008

Number of permutations of [n] having consecutive runs of increasing elements with initial elements in increasing order. a(4) = 9: `124`3, `13`24, `134`2, `14`23, `14`3`2, `2`14`3, `24`3`1, `3`14`2, `4`13`2. - Alois P. Heinz, Apr 27 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

Index entries for sequences related to factorial numbers

FORMULA

a(n) = A000142(n) - A000110(n).

E.g.f.: 1/(1-x) - exp(exp(x)-1). - Alois P. Heinz, Apr 27 2016

MAPLE

with(combinat): seq(factorial(n)-bell(n), n=0..21); # Emeric Deutsch, Apr 29 2008

MATHEMATICA

Table[n! - BellB[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

PROG

(Sage) [factorial(m) - bell_number(m) for m in range(23)]  # Zerinvary Lajos, Jul 06 2008

CROSSREFS

Cf. A000142, A000110.

Sequence in context: A231192 A133120 A194650 * A121633 A091708 A327560

Adjacent sequences:  A048739 A048740 A048741 * A048743 A048744 A048745

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)