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 A003240 Number of partially achiral rooted trees. (Formerly M1123) 1
 1, 1, 2, 4, 8, 16, 31, 62, 120, 236, 454, 884, 1697, 3275, 6266, 12020, 22935, 43788, 83325, 158516, 300914, 570794, 1081157, 2045934, 3867617, 7304149, 13783221, 25984936, 48956715, 92155376, 173376484, 325919786, 612378787, 1149777034 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..3760 (terms 1..70 from Herman Jamke) F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335. F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335. (Annotated scanned copy) FORMULA a(n) ~ c * d^n * n, where d = 1.8332964415228533737988849634129366404833316666328290543862325494628120733... is the root of the equation Sum_{k>=1} A000081(k) / d^(2*k-1) = 1 and c = 0.030410107348865811204534352170117292921782094079168428605205142049899... - Vaclav Kotesovec, Dec 13 2020 PROG (PARI) t(n)=local(A=x); if(n<1, 0, for(k=1, n-1, A/=(1-x^k+x*O(x^n))^polcoeff(A, k)); polcoeff(A, n)) {n=100; Ty2=sum(i=0, 100, t(i)*y^(2*i)); p=subst(y*Ty2/(y-Ty2), y, y+y*O(y^n)); p=Pol(p, y); r=subst(Ty2*(y+p+(p^2-subst(p, y, y^2))/(2*y))/y^2, y, x+x*O(x^n)); for(i=0, n-2, print1(polcoeff(r, i)", "))} - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008 CROSSREFS Sequence in context: A239557 A001591 A194628 * A280543 A282566 A251706 Adjacent sequences: A003237 A003238 A003239 * A003241 A003242 A003243 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008 STATUS approved

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Last modified March 23 17:27 EDT 2023. Contains 361449 sequences. (Running on oeis4.)