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 A228959 Total sum of squared lengths of ascending runs in all permutations of [n]. 3
 0, 1, 6, 32, 186, 1222, 9086, 75882, 705298, 7231862, 81160422, 990024466, 13047411482, 184788881838, 2799459801742, 45178128866282, 773829771302946, 14021761172671462, 267991492197471158, 5388234382450264002, 113692608262971520042, 2512031106415692960926 (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.: (2*exp(x)-x-2)/(x-1)^2. a(n) = (2*n+1)*a(n-1)-(n-1)*((n+2)*a(n-2)-(n-2)*a(n-3)) for n>=3, a(n) = n*(2*n-1) for n<3. a(n) ~ n! * (2*exp(1)-3)*n. - Vaclav Kotesovec, Sep 12 2013 EXAMPLE a(0) = 0: (). a(1) = 1: (1). a(2) = 6 = 4+2: (1,2), (2,1). a(3) = 32 = 9+5+5+5+5+3: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1). MAPLE a:= proc(n) option remember; `if`(n<3, n*(2*n-1), (2*n+1)*a(n-1) -(n-1)*((n+2)*a(n-2)-(n-2)*a(n-3))) end: seq(a(n), n=0..30); MATHEMATICA a[n_] := With[{k = 2}, 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=2 of A229001. Sequence in context: A259621 A026993 A238115 * A302734 A319228 A216441 Adjacent sequences: A228956 A228957 A228958 * A228960 A228961 A228962 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 09 2013 STATUS approved

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Last modified December 7 04:56 EST 2023. Contains 367629 sequences. (Running on oeis4.)