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A059117 Square array of lambda(k,n), where lambda is defined in A055203. Number of ways of placing n identifiable positive intervals with a total of exactly k starting and/or finishing points. 4
1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 6, 24, 1, 0, 0, 0, 0, 0, 114, 78, 1, 0, 0, 0, 0, 0, 180, 978, 240, 1, 0, 0, 0, 0, 0, 90, 4320, 6810, 726, 1, 0, 0, 0, 0, 0, 0, 8460, 63540, 43746, 2184, 1, 0, 0, 0, 0, 0, 0, 7560, 271170, 774000, 271194, 6558, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,18

LINKS

Table of n, a(n) for n=0..75.

FORMULA

lambda(k, n) = (lambda(k - 2, n - 1) + 2*lambda(k - 2, n - 1) + lambda(k - 2, n - 1))*k*(k - 1)/2 starting with lambda(k, 0) = 1 if k = 0 but = 0 otherwise. lambda(k, n) = sum_j[( - 1)^(k + j) * C(k, j) * ((j - 1)*j/2)^n].

EXAMPLE

Rows are: 1,0,0,0,0,0,....; 0,0,1,0,0,0,....; 0,0,1,6,6,0,....; 0,0,1,24,114,180,.... etc.

CROSSREFS

Sum of rows gives A055203. Columns include A000007, A057427, A058809, A059116. Final positive number in each row is A000680.

Sequence in context: A114629 A060251 A212528 * A196603 A267479 A285824

Adjacent sequences:  A059114 A059115 A059116 * A059118 A059119 A059120

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Jan 05 2001

STATUS

approved

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Last modified February 17 22:32 EST 2018. Contains 299297 sequences. (Running on oeis4.)