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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
OFFSET
0,3
LINKS
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);
MATHEMATICA
a[n_] := With[{k = 4}, Sum[If[n==t, 1, (n!/(t+1)!)(t(n-t+1)+1-((t+1)(n-t)+1)/(t+2))] t^k, {t, 1, n}]];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz in A229001 *)
CROSSREFS
Column k=4 of A229001.
Sequence in context: A197214 A027182 A294486 * A235397 A252971 A047643
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 10 2013
STATUS
approved