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 A183270 T(n,k) is the number of singly defective permutations of 1..n+2*k-2 with exactly k maxima. 7
 0, 3, 2, 120, 80, 15, 4760, 3552, 860, 64, 249984, 199168, 57064, 6576, 220, 17512704, 14548480, 4643712, 681984, 42112, 672, 1599330304, 1367568384, 469942528, 80506880, 6849792, 242688, 1904, 185616337920, 162107703296, 58754129408 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A singly defective permutation omits one value and repeats another value. T(1,1) is zero because there are no defective permutations of a single element. T(n,k) is divisible by n + 2*k - 2. - Andrew Howroyd, May 12 2020 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 (terms 1..36 from R. H. Hardin) FORMULA A001804(n) = Sum_{k=1..2*n+1} T(n+2-2*k, k). - Andrew Howroyd, May 12 2020 EXAMPLE Table starts: 0 3 120 4760 249984 17512704 1599330304 ... 2 80 3552 199168 14548480 1367568384 ... 15 860 57064 4643712 469942528 ... 64 6576 681984 80506880 ... 220 42112 6849792 ... 672 242688 ... 1904 ... ... Some solutions for n=4 with 2 maxima: (6,1,4,4,3,2) (4,3,1,5,6,6) (4,2,1,2,3,5) (3,2,1,6,4,3) (5,5,6,1,2,3). PROG (PARI) \\ PeaksBySig defined in A334774. T(n, k) = {my(m=n+2*k-3); (m+1)*sum(i=1, m, PeaksBySig(vector(m, j, if(i==j, 2, 1)), [k-1])[1])} \\ Andrew Howroyd, May 12 2020 CROSSREFS Columns 1..6 are A183264, A183265, A183266, A183267, A183268, A183269. Cf. A001804, A008303, A334774. Sequence in context: A323745 A109899 A002297 * A152017 A076931 A076932 Adjacent sequences: A183267 A183268 A183269 * A183271 A183272 A183273 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jan 03 2011 STATUS approved

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Last modified September 25 02:38 EDT 2023. Contains 365582 sequences. (Running on oeis4.)