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 A232475 Number of preferential arrangements of n labeled elements when at least k=4 elements per rank are required. 11
 1, 0, 0, 0, 1, 1, 1, 1, 71, 253, 673, 1585, 38149, 277707, 1402831, 5923503, 85577571, 937629969, 7475614341, 48939413477, 587610659505, 7906296686903, 87384175023995, 804959532778571, 9729015122635103, 144711323234918941, 2009073351016603121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 I. Mezo, Periodicity of the last digits of some combinatorial sequences, arXiv preprint arXiv:1308.1637 [math.CO], 2013. FORMULA E.g.f.: 1/(2 + x - exp(x) + x^2/2 + x^3/6). - Vaclav Kotesovec, Aug 02 2014 a(n) ~ n! / ((1+r^3/6) * r^(n+1)), where r = 1.97615974210650519398... is the root of the equation 2 + r - exp(r) + r^2/2 + r^3/6 = 0. - Vaclav Kotesovec, Aug 02 2014 a(0) = 1; a(n) = Sum_{k=4..n} binomial(n,k) * a(n-k). - Ilya Gutkovskiy, Feb 09 2020 MAPLE b:= proc(n) b(n):= `if`(n=0, 1, add(b(n-j)/j!, j=4..n)) end: a:= n-> n!*b(n): seq(a(n), n=0..30); # Alois P. Heinz, Jul 29 2014 MATHEMATICA CoefficientList[Series[1/(2 + x - E^x + x^2/2 + x^3/6), {x, 0, 20}], x]*Range[0, 20]! (* Vaclav Kotesovec, Aug 02 2014 *) CROSSREFS Cf. A032032, A102233. Cf. column k=4 of A245732. Sequence in context: A123038 A325079 A142325 * A243579 A142013 A033240 Adjacent sequences: A232472 A232473 A232474 * A232476 A232477 A232478 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 27 2013 EXTENSIONS More terms from Alois P. Heinz, Jul 29 2014 STATUS approved

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Last modified August 13 02:28 EDT 2024. Contains 375113 sequences. (Running on oeis4.)