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%I #15 Sep 19 2022 04:52:34
%S 2,36,210,6750,8120,459620,2067170,20522250,22318758,2905171038,
%T 3098543448,554652370272,584150230092,612299943684,2556925522866,
%U 768804781750434,797490150102074,297862797402850394,307475819473818710,316760108055672710,325739683035302510,176916612931176848990
%N a(n) = (2nd elementary symmetric function of {1/1, 1/2, ..., 1/n})*(lcm(S))^2, where S = {1,2,...,n}.
%H Robert Israel, <a href="/A025531/b025531.txt">Table of n, a(n) for n = 2..1150</a>
%p g:= gfun:-rectoproc({(-n^2-4*n-4)*s(n+1)+(3*n^2+15*n+19)*s(n+2)+(-3*n^2-18*n-27)*s(n+3)+(n^2+7*n+12)*s(n+4), s(0) = 0, s(1) = 0, s(2) = 1/2, s(3) = 1},s(n),remember):
%p f:= n -> g(n)*ilcm($1..n)^2:
%p map(f, [$2..100]); # _Robert Israel_, Aug 10 2018
%t nmax = 100;
%t T = RecurrenceTable[{(-n^2 - 4*n - 4)*s[n+1] + (3*n^2 + 15*n + 19)*s[n+2] + (-3*n^2 - 18*n - 27)*s[n+3] + (n^2 + 7*n + 12)*s[n+4] == 0, s[0] == 0, s[1] == 0, s[2] == 1/2}, s, {n, 0, nmax}];
%t f[n_] := T[[n+1]]*(LCM @@ Range[n])^2;
%t Map[f, Range[2, nmax]] (* _Jean-François Alcover_, Sep 19 2022, after _Robert Israel_ *)
%K nonn
%O 2,1
%A _Clark Kimberling_
%E Offset corrected and more terms from _Robert Israel_, Aug 10 2018
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