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 A324362 Total number of occurrences of k in the (signed) displacement sets of all permutations of [n+k] divided by k!; square array A(n,k), n>=0, k>=0, read by antidiagonals. 14
 0, 0, 1, 0, 1, 1, 0, 1, 3, 4, 0, 1, 5, 13, 15, 0, 1, 7, 28, 67, 76, 0, 1, 9, 49, 179, 411, 455, 0, 1, 11, 76, 375, 1306, 2921, 3186, 0, 1, 13, 109, 679, 3181, 10757, 23633, 25487, 0, 1, 15, 148, 1115, 6576, 29843, 98932, 214551, 229384, 0, 1, 17, 193, 1707, 12151, 69299, 307833, 1006007, 2160343, 2293839 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened Wikipedia, Permutation FORMULA E.g.f. of column k: (1-exp(-x))/(1-x)^(k+1). A(n,k) = -1/k! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+k-j)!. A(n,k) = A306234(n+k,k). EXAMPLE Square array A(n,k) begins:     0,    0,     0,     0,     0,      0,      0, ...     1,    1,     1,     1,     1,      1,      1, ...     1,    3,     5,     7,     9,     11,     13, ...     4,   13,    28,    49,    76,    109,    148, ...    15,   67,   179,   375,   679,   1115,   1707, ...    76,  411,  1306,  3181,  6576,  12151,  20686, ...   455, 2921, 10757, 29843, 69299, 142205, 266321, ... MAPLE A:= (n, k)-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!: seq(seq(A(n, d-n), n=0..d), d=0..12); CROSSREFS Columns k=0-10 give: A002467, A180191(n+1), A324352, A324353, A324354, A324355, A324356, A324357, A324358, A324359, A324360. Rows n=0-3 give: A000004, A000012, A005408, A056107(k+1). Main diagonal gives A324361. Cf. A306234. Sequence in context: A170952 A194587 A175646 * A073234 A123685 A124917 Adjacent sequences:  A324359 A324360 A324361 * A324363 A324364 A324365 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Feb 23 2019 STATUS approved

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Last modified September 27 15:29 EDT 2020. Contains 337383 sequences. (Running on oeis4.)