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A244312 Triangle read by rows: T(n,k) is the number of single loop solutions formed by n proper arches (connecting an odd and even vertice from 1 to 2n) above the x axis, k arches above the x axis connecting an odd vertice to a higher even vertice and a rainbow of n arches below the x axis. 1
1, 0, 1, 0, 2, 0, 0, 2, 4, 0, 0, 4, 16, 4, 0, 0, 4, 48, 60, 8, 0, 0, 8, 160, 384, 160, 8, 0, 0, 8, 368, 1952, 2176, 520, 16, 0, 0, 16, 1152, 9648, 18688, 9648, 1152, 16, 0, 0, 16, 2432, 37008, 132640, 141680, 45504, 3568, 32, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Sum of row n = (n-1)!

LINKS

Table of n, a(n) for n=1..55.

FORMULA

T(n,k)= (k+ floor((-1)^(n-1)/2)(T(n-1,k))+(n-k- floor((-1)^(n-1)/2)(T(n-1,k-1)); n=>2, 1<=k<=n, T(1,1)=1, T(n,0)=0, T(n,n+1)=0.

EXAMPLE

Triangle T(n,k) begins:

n\k  1     2     3     4     5     6     7     8

1    1

2    0     1

3    0     2     0

4    0     2     4     0

5    0     4    16     4     0

6    0     4    48    60     8     0

7    0     8   160   384   160     8    0

8    0     8   368  1952  2176   520   16    0

T(4,3)=4 [top 14,23,56,78; bottom 18,27,36,45] [top 16,25,34,78; bottom 18,27,36,45] [top 12,34,58,67; bottom 18,27,36,45] [top 12,38,47,56; bottom 18,27,36,45]

CROSSREFS

Sequence in context: A195581 A020474 A135589 * A158122 A028641 A141416

Adjacent sequences:  A244309 A244310 A244311 * A244313 A244314 A244315

KEYWORD

nonn,tabl

AUTHOR

Roger Ford, Jul 02 2014

STATUS

approved

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Last modified February 20 03:12 EST 2018. Contains 299357 sequences. (Running on oeis4.)