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%I #22 Apr 08 2018 17:11:54
%S 0,1,7,63,736,10625,182736,3647119,82837504,2109289329,59500000000,
%T 1841557146671,62041198952448,2259914256880657,88499197217837056,
%U 3707501605224609375,165444235911082541056,7834451891982365825441,392371124973096027488256
%N Number of ascending runs in {1,...,n}^n.
%H Alois P. Heinz, <a href="/A229078/b229078.txt">Table of n, a(n) for n = 0..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>
%F a(n) = n^(n-1)*(n*(n+2)-1)/2 for n>0, a(0) = 0.
%F 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).
%F a(n) = A062023(n) + A066274(n) for n>0.
%e a(1) = 1: [1].
%e a(2) = 7 = 2+2+1+2: [1,1], [2,1], [1,2], [2,2].
%p a:= n-> `if`(n=0, 0, n^(n-1)*(n*(n+2)-1)/2):
%p seq(a(n), n=0..25);
%Y Main diagonal of A229079.
%Y Cf. A062023 (nondescending runs), A066274.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 12 2013
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