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A121704 Number of separable involutions. 1
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; refs; listen; history; internal format)
OFFSET

1,2

COMMENTS

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 * A049144 A049131 A084078

Adjacent sequences:  A121701 A121702 A121703 * A121705 A121706 A121707

KEYWORD

nonn

AUTHOR

Vince Vatter (vince(AT)mcs.st-and.ac.uk), Aug 16 2006

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Last modified February 13 03:07 EST 2012. Contains 205435 sequences.