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A064314 Total length of longest increasing runs in all permutations of n elements. 2
1, 3, 12, 55, 299, 1900, 13942, 115932, 1078361, 11092265, 125040100, 1532995992, 20310212672, 289186696338, 4404156016584, 71441907922793, 1229835421590959, 22393298253477006, 430019590699868644, 8685717780508953928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200 (first 100 terms from Max Alekseyev)

FORMULA

a(n) = Sum_{k=1..n} k*A008304(n,k). - Max Alekseyev, May 22 2012

MAPLE

b:= proc(u, o, t, k) option remember; `if`(t=k, (u+o)!,

      `if`(max(t, u)+o<k, 0, add(b(u+j-1, o-j, t+1, k), j=1..o)+

      add(b(u-j, o+j-1, 1, k), j=1..u)))

    end:

a:= n-> add(b(0, n, 0, k), k=1..n) -n*b(0, n, 0, n+1):

seq(a(n), n=1..25);  # Alois P. Heinz, Oct 16 2013

MATHEMATICA

nn=30; f[list_]:=Total[Table[list[[i]]*i, {i, 1, Length[list]}]]; a[r_]:=Apply[Plus, Table[Normal[Series[y x^(r+1)/(1-Sum[y x^i, {i, 1, r}]), {x, 0, nn}]][[n]]/(n+r)!, {n, 1, nn-r}]]/.y->-1; Map[f, Map[Select[#, #>0&]&, Transpose[Prepend[Table[Drop[Range[0, nn]! CoefficientList[Series[1/(1-x-a[n+1])-1/(1-x-a[n]), {x, 0, nn}], x], 1], {n, 1, 28}], Table[1, {nn}]]]]] (* Geoffrey Critzer, Feb 25 2014 *)

CROSSREFS

This sequence treats runs of adjacent elements, A003316 treats subsequences of not necessarily adjacent elements.

Sequence in context: A120920 A179487 A263533 * A185630 A284843 A107318

Adjacent sequences:  A064311 A064312 A064313 * A064315 A064316 A064317

KEYWORD

nonn

AUTHOR

David W. Wilson, Sep 07 2001

STATUS

approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)