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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 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=0..k} (-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. MATHEMATICA A[ n_, k_] := If[n < 1 || k < 1, Boole[n == 0 && k == 0], n! k! Coefficient[ Normal[ Series[ Sum[ Exp[-x z] (x z)^m/m! Exp[y z m (m - 1)/2], {m, 0, n}], {z, 0, n + k}]], x^n y^k z^(n + k)]]; (* Michael Somos, Jul 17 2019 *) 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 A318458 A267479 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 August 17 16:57 EDT 2019. Contains 326059 sequences. (Running on oeis4.)