The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A317327 Number T(n,k) of permutations of [n] with exactly k distinct lengths of increasing runs; triangle T(n,k), n>=0, 0<=k<=A003056(n), read by rows. 5
 1, 0, 1, 0, 2, 0, 2, 4, 0, 7, 17, 0, 2, 118, 0, 82, 436, 202, 0, 2, 3294, 1744, 0, 1456, 18164, 20700, 0, 1515, 140659, 220706, 0, 50774, 1096994, 2317340, 163692, 0, 2, 10116767, 27136103, 2663928, 0, 3052874, 94670868, 328323746, 52954112, 0, 2, 1021089326, 4317753402, 888178070 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Rows n = 0..60, flattened FORMULA T(n*(n+1)/2,n) = A317273(n). Sum_{k=0..floor((sqrt(1+8*n)-1)/2)} k * T(n,k) = A317328(n). EXAMPLE T(4,1) = 7: 1234, 1324, 1423, 2314, 2413, 3412, 4321. Triangle T(n,k) begins:   1;   0,       1;   0,       2;   0,       2,        4;   0,       7,       17;   0,       2,      118;   0,      82,      436,       202;   0,       2,     3294,      1744;   0,    1456,    18164,     20700;   0,    1515,   140659,    220706;   0,   50774,  1096994,   2317340,   163692;   0,       2, 10116767,  27136103,  2663928;   0, 3052874, 94670868, 328323746, 52954112; MAPLE b:= proc(u, o, t, s) option remember;       `if`(u+o=0, x^(nops(s union {t})-1),        add(b(u-j, o+j-1, 1, s union {t}), j=1..u)+        add(b(u+j-1, o-j, t+1, s), j=1..o))     end: T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 0\$2, {})): seq(T(n), n=0..16); CROSSREFS Columns k=0-1 give: A000007, A317329. Row sums give A000142. Cf. A000217, A003056, A097591, A097592, A123125, A218868, A317273. Sequence in context: A143507 A071961 A172040 * A120557 A092594 A092741 Adjacent sequences:  A317324 A317325 A317326 * A317328 A317329 A317330 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Jul 25 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)