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 A230055 Number of permutations of [n] in which the longest increasing run has length 7. 3
 1, 14, 181, 2360, 32010, 456720, 6881160, 109546009, 1841298059, 32629877967, 608572228291, 11923667699474, 244964063143590, 5267496652725480, 118348438201424761, 2773714509551524351, 67705791536824698266, 1718769199589362743761, 45314525515737783596251 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 7..200 FORMULA a(n) = A230051(n) - A177553(n). E.g.f.: 1/Sum_{n>=0} (8*n+1-x)*x^(8*n)/(8*n+1)! - 1/Sum_{n>=0} (7*n+1-x)*x^(7*n)/(7*n+1)!. EXAMPLE a(7) = 1: 1234567. a(8) = 14: 12345687, 12345786, 12346785, 12356784, 12456783, 13456782, 21345678, 23456781, 31245678, 41235678, 51234678, 61234578, 71234568, 81234567. MAPLE b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,       `if`(t b(n, 0, 0, 7)-b(n, 0, 0, 6): seq(a(n), n=7..30); MATHEMATICA b[u_, o_, t_, k_] := b[u, o, t, k] = If[u + o == 0, 1, If[t < k - 1, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}], 0] + Sum[b[u - j, o + j - 1, 0, k], {j, 1, u}]]; a[n_] := b[n, 0, 0, 7] - b[n, 0, 0, 6]; Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Jul 19 2018, after Alois P. Heinz *) CROSSREFS Column k=7 of A008304. Sequence in context: A125471 A132010 A126866 * A133286 A163416 A162783 Adjacent sequences:  A230052 A230053 A230054 * A230056 A230057 A230058 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 07 2013 STATUS approved

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Last modified March 30 15:29 EDT 2020. Contains 333127 sequences. (Running on oeis4.)