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%I #17 Dec 31 2018 14:15:06
%S 1,1,3,6,14,28,68,148,358,845,2061,5018,12458,30922,77557,195154,
%T 493809,1253614,3195210,8166758,20935826,53799072,138571332,357647566,
%U 924846881,2395702829,6215779536,16150985916,42024260088,109485000778
%N CIK transform of partition numbers A000041.
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H P. Flajolet and M. Soria, <a href="http://algo.inria.fr/flajolet/Publications/cycle2.ps.gz">The Cycle Construction</a>. In SIAM J. Discr. Math., vol. 4 (1), 1991, pp. 58-60.
%H P. Flajolet and M. Soria, <a href="/A055890/a055890.pdf">The Cycle Construction</a>. [pdf file]
%t nmax = 30;
%t f[x_] = 1/Product[1 - x^n, {n, 1, nmax}] - 1;
%t gf = 1+Sum[(EulerPhi[n]/n)*Log[1/(1 - f[x^n])] + O[x]^nmax, {n, 1, nmax}];
%t CoefficientList[gf, x] (* _Jean-François Alcover_, Jul 29 2018, from PARI *)
%o (PARI)
%o N = 66; x = 'x + O('x^N);
%o f(x) = 1 / prod(n=1,N, 1-x^n ) - 1; \\ A055890
%o gf = 1 + sum(n=1,N, eulerphi(n)/n*log(1/(1-f(x^n))) );
%o v = Vec(gf)
%o /* _Joerg Arndt_, Jan 21 2013 */
%Y Cf. A055889, A000142.
%K nonn
%O 0,3
%A _Christian G. Bower_, Jun 09 2000
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