id:A121704 - OEIS Search Results

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Number of separable involutions.

+0
2

1, 2, 4, 10, 24, 64, 166, 456, 1234, 3454, 9600, 27246, 77132, 221336, 635078, 1839000, 5331274, 15555586, 45465412, 133517130, 392841336, 1160033656, 3432015726, 10182891552, 30267591290, 90177226062, 269117947728 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`The separable permutations are those avoiding 2413 and 3142 and are counted by the large Schroeder numbers (A006318).`
	LINKS	`R. Brignall, S. Huczynska and V. Vatter, Simple permutations and algebraic generating functions, arXiv:math.CO/0608391.`
	FORMULA	`G.f. satisfies x^2f^4 + (x^3+3x^2+x-1)f^3 + (3x^3+6x^2-x)f^2 + (3x^3+7x^2-x-1)f +x^3+3x^2+x=0.`
	EXAMPLE	`a(4)=4 because of the 26 involutions of length 4 only two are not separable, 35142 and 42513.`
	CROSSREFS	`Cf. A121703.` `Sequence in context: A124499 A132220 A007874 this_sequence A049144 A049131 A084078` `Adjacent sequences: A121701 A121702 A121703 this_sequence A121705 A121706 A121707`
	KEYWORD	`nonn`
	AUTHOR	`Vince Vatter (vince(AT)mcs.st-and.ac.uk), Aug 16 2006`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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