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 A006961 Number of mappings from n points to themselves with in-degree <= 2. (Formerly M2584) 4
 1, 1, 3, 6, 15, 31, 75, 164, 388, 887, 2092, 4884, 11599, 27443, 65509, 156427, 375263, 901353, 2171313, 5237581, 12658815, 30633725, 74238228, 180106656, 437437445, 1063425655, 2587564434, 6301175326, 15356071604, 37448674536 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS N. G. de Bruijn, D. A. Klarner, Multisets of aperiodic cycles, SIAM J. Algebraic Discrete Methods, 3 (1982), no. 3, 359-368. MR0666861(84i:05008). FORMULA 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 MATHEMATICA 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 *) CROSSREFS Cf. A001190. Sequence in context: A244710 A244711 A244712 * A316219 A034740 A305839 Adjacent sequences:  A006958 A006959 A006960 * A006962 A006963 A006964 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Jean-François Alcover, Dec 03 2015 STATUS approved

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Last modified December 18 09:25 EST 2018. Contains 318219 sequences. (Running on oeis4.)