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%I M2584 #20 Dec 04 2015 02:48:19
%S 1,1,3,6,15,31,75,164,388,887,2092,4884,11599,27443,65509,156427,
%T 375263,901353,2171313,5237581,12658815,30633725,74238228,180106656,
%U 437437445,1063425655,2587564434,6301175326,15356071604,37448674536
%N Number of mappings from n points to themselves with in-degree <= 2.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H N. G. de Bruijn, D. A. Klarner, <a href="http://dx.doi.org/10.1137/0603037">Multisets of aperiodic cycles</a>, SIAM J. Algebraic Discrete Methods, 3 (1982), no. 3, 359-368. MR0666861(84i:05008).
%F Let T(x) = x+x^2+x^3+2*x^4+3*x^5+6*x^6+11*x^7+ ... be the g.f. for A001190. Then the g.f. here is 1/(Prod_{k=1..oo} (1-T(x^k))). - _N. J. A. Sloane_, Mar 25 2014
%t max = 30; (* w(n) is A001190(n) *) w[0]=0; w[1]=1; w[n_] := w[n] = If[ OddQ[n], Sum[w[k]*w[n-k], {k, 1, (n-1)/2}], Sum[w[k]*w[n-k], {k, 1, n/2 - 1}] + (1/2)*w[n/2]*(1 + w[n/2]) ]; T[x_] := Sum[w[n] x^n, {n, 0, max}]; s = 1/Product[1-T[x^k], {k, 1, max}] + O[x]^max; CoefficientList[s, x] (* _Jean-François Alcover_, Dec 03 2015 *)
%Y Cf. A001190.
%K nonn,easy,nice
%O 0,3
%A _Simon Plouffe_
%E More terms from _Jean-François Alcover_, Dec 03 2015
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