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%I M3504 #24 Sep 15 2024 01:57:43
%S 1,1,4,15,62,271,1247,5938,29113,145815,743384,3844314,20118681,
%T 106348391,567002169,3045455865,16463622763,89509216860,489103356753,
%U 2684663659765,14795752770278,81841297482116,454202999050433,2528381760697852
%N Number of skeins with 2n+1 edges.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. C. Read, <a href="http://dx.doi.org/10.1007/BF02188172">On the enumeration of a class of plane multigraphs</a>, Aequat. Math. 31 (1986) no 1, 47-63.
%o (PARI) { my(s =y); for(loop=1,18, my(p = 1); forstep(i= 1,2*loop-1,2, my(sigmai = polcoef(s,i,y)) ; if(i==2*loop-1, print1(sigmai,", "); ) ; my(n=0, tmp = 0); while(i*n <=2*loop-1, my(ff = 1); for(k=1,n, ff *= (-sigmai-k+1)/k ; ) ; tmp += ff*(-y)^(i*n) ; n++ ; ) ; p *= tmp ; ) ; my(b = y-s); forstep(i=1,2*loop-1,2, b += polcoef(p,i,y)*y^i ; ) ; s = y ; for(r=0,loop-1, for(i=0,2*loop+1, s += polcoef(b^(3+2*r),i,y)*y^i ; ) ; ) ; ) ; } \\ _R. J. Mathar_, Apr 24 2006
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _R. J. Mathar_, Apr 24 2006
%E More terms from _Sean A. Irvine_, Nov 07 2017