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A228994 Total sum of the 4th powers of lengths of ascending runs in all permutations of [n]. 3
0, 1, 18, 152, 1110, 8254, 66050, 578466, 5557246, 58381646, 667481754, 8262618730, 110195259446, 1576108225446, 24075493095346, 391282065519074, 6742907753730030, 122830141805635966, 2358555332361509066, 47617194132209848026, 1008436738991020480294 (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.: (exp(x)*(12*x^2-12*x+14)-x-14)/(x-1)^2.

a(n) ~ n! * (14*exp(1)-15)*n. - Vaclav Kotesovec, Sep 12 2013

MAPLE

a:= proc(n) option remember; `if`(n<3, [0, 1, 18][n+1],

      ((12*n^3-42*n^2+38*n+7)*a(n-1)-(n-1)*(6*n^3-12*n^2+n+14)*a(n-2)

       +(n-1)*(n-2)*(6*n^2-12*n+7)*a(n-3))/(6*n^2-24*n+25))

    end:

seq(a(n), n=0..30);

CROSSREFS

Column k=4 of A229001.

Sequence in context: A197214 A027182 A294486 * A235397 A252971 A047643

Adjacent sequences:  A228991 A228992 A228993 * A228995 A228996 A228997

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 10 2013

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)