A126429 Number of permutations of the numbers 1 through 2n satisfying the "Alex Fink" condition: there is one and only one partial sum in each interval (k(n+1),(k+1)(n+1)] for 0<=k<2n-1.

2, 8, 96, 1344, 30880, 957696, 38918656, 1923336192, 124407313920, 9362791403520, 61463178391552, 91501241391071232, 11493240430821187584

Offset: 1

Author

Kevin Saff (kevin.saff(AT)gmail.com), Mar 11 2007

Keywords

• more
• nonn

Examples

			a(2)=8 since there are eight permutations of (1,2,3,4) satisfying the Fink condition: (1,3,4,2), (1,4,2,3), (1,4,3,2), (2,4,1,3) and their mirror images.
		

References

• R. K. Guy, Building Barrycades, preprint, 2006
• R. K. Guy, Building Barrycades and Constructing Corrals, in "Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rogers", ed. Thane Plambeck and Tomas Rokicki, MAA Press, 2020, pp. 11-18

Extensions

a(9)-a(13) from Don Knuth, Aug 24 2020