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%I #26 Oct 06 2019 07:48:00
%S 1,1,1,2,6,27,160,1183,10477,108149,1275024,16903440,248915119,
%T 4031045212,71202358081,1362297883463,28066342411395,619474462826562,
%U 14583353438928682,364748466791800669,9658964416375216576,269978766441123241685,7943074999430019396711
%N Shifts left 2 places under "CIJ" (necklace, indistinct, labeled) transform.
%H Alois P. Heinz, <a href="/A032186/b032186.txt">Table of n, a(n) for n = 1..426</a>
%F E.g.f. A(x) satisfies differential equation A''(x)=log(1/(1-A(x)), A'(0)=1, A''(0)=1. - _Vladimir Kruchinin_, Nov 18 2011
%F a(n) = n!*b(n), b(n) = b(n-2)*(n-2) + sum(i=0..n-4, b(i+3)*(i+1)*(i+2)*(i+3)*b(n-3-i)))/(n*(n-1)*(n-2)) n > 0, b(1)=1, b(2)=1/2. - _Vladimir Kruchinin_, Nov 18 2011
%t CIJ[p_] := -Log[1 - p];
%t seq[n_] := Module[{p}, p = x + O[x]^(Mod[n, 2] + 1); Do[p = Integrate[1 + Integrate[1 + CIJ[p], x], x], {i, 1, n/2}]; CoefficientList[p/x, x]* Range[n]!];
%t seq[23] (* _Jean-François Alcover_, Oct 06 2019, after _Andrew Howroyd_ *)
%o (Maxima)
%o a(n):=if n<3 then 1/n! else (a(n-2)*(n-2)+sum(a(i+3)*(i+1)*(i+2)*(i+3)*a(n-3-i),i,0,n-4))/(n*(n-1)*(n-2));
%o makelist(n!*a(n),n,1,17); /* _Vladimir Kruchinin_, Nov 18 2011 */
%o (PARI)
%o CIJ(p)={-log(1-p)}
%o seq(n)={my(p=x+O(x*x^(n%2))); for(i=1, n\2, p=intformal(1 + intformal(1 + CIJ(p)))); Vec(serlaplace(p))} \\ _Andrew Howroyd_, Sep 19 2018
%K nonn,eigen
%O 1,4
%A _Christian G. Bower_
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