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 A092582 Triangle read by rows: T(n,k) is the number of permutations p of [n] having length of first run equal to k. 8
 1, 1, 1, 3, 2, 1, 12, 8, 3, 1, 60, 40, 15, 4, 1, 360, 240, 90, 24, 5, 1, 2520, 1680, 630, 168, 35, 6, 1, 20160, 13440, 5040, 1344, 280, 48, 7, 1, 181440, 120960, 45360, 12096, 2520, 432, 63, 8, 1, 1814400, 1209600, 453600, 120960, 25200, 4320, 630, 80, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums are the factorial numbers (A000142). First column is A001710. T(n,k) = number of permutations of [n] in which 1,2,...,k is a subsequence but 1,2,...,k,k+1 is not. Example: T(4,2)=8 because 1324, 1342, 1432, 4132, 3124, 3142, 3412 and 4312, are the only permutations of [4] in which 12 is a subsequence but 123 is not. - Emeric Deutsch, Nov 12 2004 T(n,k) is the number of deco polyominoes of height n with k cells in the last column. (A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column). - Emeric Deutsch, Jan 06 2005 T(n,k) is the number of permutations p of [n] for which the smallest i such that p(i)0. - Alois P. Heinz, Jun 19 2017 EXAMPLE T(4,3) = 3 because 1243, 1342 and 2341 are the only permutations of [4] having length of first run equal to 3.      1;      1,    1;      3,    2,   1;     12,    8,   3,   1;     60,   40,  15,   4,  1;    360,  240,  90,  24,  5,  1;   2520, 1680, 630, 168, 35,  6,  1; MATHEMATICA Drop[Drop[Abs[Map[Select[#, # < 0 &] &, Map[Differences, nn = 10; Range[0, nn]! CoefficientList[Series[(Exp[y x] - 1)/(1 - x), {x, 0, nn}], {x, y}]]]], 1], -1] // Grid (* Geoffrey Critzer, Jun 18 2017 *) PROG (PARI) {T(n, k) = if( n<1 || k>n, 0, k==n, 1, n! * k /(k+1)!)}; /* Michael Somos, Jun 25 2017 */ (GAP) Flat(List([1..11], n->Concatenation([1], List([1..n-1], k->Factorial(n)*k/Factorial(k+1))))); # Muniru A Asiru, Jun 10 2018 CROSSREFS Cf. A000166. Cf. A002260. - Gary W. Adamson, Feb 22 2012 Cf. A092956, A130477. Sequence in context: A115085 A110616 A059418 * A213262 A280512 A068440 Adjacent sequences:  A092579 A092580 A092581 * A092583 A092584 A092585 KEYWORD nonn,tabl AUTHOR Emeric Deutsch and Warren P. Johnson (wjohnson(AT)bates.edu), Apr 10 2004 STATUS approved

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Last modified February 17 12:10 EST 2019. Contains 320219 sequences. (Running on oeis4.)