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A229003 Total sum of cubed lengths of ascending runs in all permutations of [n]. 3
0, 1, 10, 66, 426, 2964, 22818, 195000, 1842234, 19120260, 216604194, 2662063728, 35297775930, 502460232684, 7644691295970, 123824090015544, 2127644969464698, 38659776477571860, 740692592536389474, 14924674961053224000, 315523813278300959994 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: (6*exp(x)*(x-1)+x+6)/(x-1)^2.

a(n) ~ n! * 7*n. - Vaclav Kotesovec, Sep 12 2013

MAPLE

a:= proc(n) option remember; `if`(n<3, [0, 1, 10][n+1],

      ((2*n^2-3*n-1)*a(n-1) -(n-1)*(n^2-2)*a(n-2)

       +(n-2)*(n-1)^2*a(n-3) )/(n-2))

    end:

seq(a(n), n=0..25);

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(6 Exp[x](x-1)+x+6)/(x-1)^2, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 26 2019 *)

CROSSREFS

Column k=3 of A229001.

Sequence in context: A033504 A163615 A232062 * A117305 A250790 A231886

Adjacent sequences:  A229000 A229001 A229002 * A229004 A229005 A229006

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 10 2013

STATUS

approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)