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%I #8 Jan 05 2021 22:07:47
%S 1,2,4,2,-74,-916,-8672,-73564,-542852,-2595016,18348496,906083672,
%T 21021502984,406255974032,7157641045696,116383645516784,
%U 1681549859135248,18311613681506336,-3332917116147392
%N Alternating row sums of triangle A046089 (S1p(3)).
%F a(n) = Sum_{m=1..n} A046089(n,m)*(-1)^(m-1), n >= 1.
%F E.g.f.: 1 - exp(-x*(2-x)/(2*(1-x)^2)). Cf. e.g.f. first column of A046089.
%F a(n) = (3*n-4)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (n-3)*(n-2)*(n-1)*a(n-3). - _Vaclav Kotesovec_, Oct 09 2013
%F Lim sup n->infinity |a(n)|/(2*n^(n-1/6)*exp(-n^(1/3)/4+3*n^(2/3)/4-n+1/3)/sqrt(3)) = 1. - _Vaclav Kotesovec_, Oct 09 2013
%t Rest[CoefficientList[Series[1-E^(-x*(2-x)/(2*(1-x)^2)), {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Oct 09 2013 *)
%Y Cf. A049377 (row sums of A046089).
%K sign,easy
%O 1,2
%A _Wolfdieter Lang_ Oct 12 2007
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