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Revision History for A145902

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A145902

Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n.
(history; published version)

#5 by Bruno Berselli at Wed Sep 16 05:03:07 EDT 2020

STATUS

proposed

approved

#4 by Michel Marcus at Wed Sep 16 03:45:45 EDT 2020

STATUS

editing

proposed

#3 by Michel Marcus at Wed Sep 16 03:45:42 EDT 2020

FORMULA

E.g.f. : ((1 + x)*z - exp(z))/(x*exp(2*z) - (1 + x)) = 1 + x*z + (1 + 4*x + 4*x^2)*z^2/2! + (1 + 14*x + 36*x^2 + 24*x^3)*z^3/3! + ... . Row sums A080254.! + ... .

Row sums A080254.

CROSSREFS

Cf. A019538 (f-vectors type A permutohedra), A080254 (row sums), A066094 (h-vectors type D permutohedra), A145901 (f-vectors type B permutohedra).

STATUS

approved

editing

#2 by Russ Cox at Sat Mar 31 13:47:34 EDT 2012

	AUTHOR	`_Peter Bala (pbala(AT)toucansurf.com), _, Oct 29 2008`
	EXTENSIONS	`Corrected typo. - . - _Peter Bala (pbala(AT)toucansurf.com), _, Oct 31 2008`

Discussion
Sat Mar 31	13:47	OEIS Server: https://oeis.org/edit/global/892

#1 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

	NAME	`Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n.`
	DATA	`1, 1, 1, 1, 4, 4, 1, 14, 36, 24, 1, 48, 240, 384, 192, 1, 162, 1440, 4160, 4800, 1920, 1, 536, 8216, 38400, 76800, 69120, 23040, 1, 1738, 45528, 326032, 1008000, 1532160, 1128960, 322560, 1, 5536, 247456, 2634240, 11854080, 27095040, 33116160`
	OFFSET	`0,5`
	COMMENTS	`The root systems of type D_n are only defined for n >= 2. It is convenient to add two initial rows to the array to give a lower triangular array. See A066094 for the corresponding array of h-vectors of type D permutohedra.`
	FORMULA	`E.g.f. : ((1 + x)z - exp(z))/(xexp(2z) - (1 + x)) = 1 + xz + (1 + 4x + 4x^2)z^2/2! + (1 + 14x + 36x^2 + 24x^3)*z^3/3! + ... . Row sums A080254.`
	EXAMPLE	`The triangle begins` `n\k\|..0.....1.....2.....3.....4.....5` `=====================================` `0..\|..1` `1..\|..1.....1` `2..\|..1.....4.....4` `3..\|..1....14....36....24` `4..\|..1....48...240...384...192` `5..\|..1...162..1440..4160..4800..1920` `...`
	CROSSREFS	`A019538 (f-vectors type A permutohedra), A080254 (row sums), A066094 (h-vectors type D permutohedra), A145901 (f-vectors type B permutohedra).`
	KEYWORD	`easy,nonn,tabl`
	AUTHOR	`Peter Bala (pbala(AT)toucansurf.com), Oct 29 2008`
	EXTENSIONS	`Corrected typo. - Peter Bala (pbala(AT)toucansurf.com), Oct 31 2008`
	STATUS	`approved`

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Last modified August 18 14:27 EDT 2024. Contains 375269 sequences. (Running on oeis4.)