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 A229078 Number of ascending runs in {1,...,n}^n. 3
 0, 1, 7, 63, 736, 10625, 182736, 3647119, 82837504, 2109289329, 59500000000, 1841557146671, 62041198952448, 2259914256880657, 88499197217837056, 3707501605224609375, 165444235911082541056, 7834451891982365825441, 392371124973096027488256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 Eric Weisstein's World of Mathematics, Lambert W-Function Wikipedia, Lambert W function FORMULA a(n) = n^(n-1)*(n*(n+2)-1)/2 for n>0, a(0) = 0. E.g.f.: 1/2*W(-x)*(W(-x)^3+W(-x)^2-W(-x)-2)/(1+W(-x))^3, W(x) Lambert's function (principal branch). a(n) = A062023(n) + A066274(n) for n>0. EXAMPLE a(1) = 1: [1]. a(2) = 7 = 2+2+1+2: [1,1], [2,1], [1,2], [2,2]. MAPLE a:= n-> `if`(n=0, 0, n^(n-1)*(n*(n+2)-1)/2): seq(a(n), n=0..25); CROSSREFS Main diagonal of A229079. Cf. A062023 (nondescending runs), A066274. Sequence in context: A185106 A275577 A049464 * A346683 A084063 A184141 Adjacent sequences:  A229075 A229076 A229077 * A229079 A229080 A229081 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 12 2013 STATUS approved

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Last modified January 20 08:49 EST 2022. Contains 350469 sequences. (Running on oeis4.)