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P-graphs with 2n edges.
(Formerly M1774)
0

%I M1774 #17 Nov 07 2017 18:39:21

%S 1,2,7,26,114,512,2427,11794,58787,298188,1535962,8009527,42209709,

%T 224435066,1202611161,6487520874,35204691958,192042016789,

%U 1052495823168,5792479501760,32000066582116,177388902951224,986412534845206,5500872578870102

%N P-graphs with 2n 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) { s =y ; for(loop=1,18, p = 1 ; forstep(i= 1,2*loop-1,2, sigmai = polcoeff(s,i,y) ; n=0 ; tmp = 0 ; while(i*n <=2*loop-1, ff = 1 ; for(k=1,n, ff *= (-sigmai-k+1)/k ; ) ; tmp += ff*(-y)^(i*n) ; n++ ; ) ; p *= tmp : ) ; print1(polcoeff(p,2*loop-2,y),",") ; b = y-s ; forstep(i=1,2*loop-1,2, b += polcoeff(p,i,y)*y^i ; ) ; s = y ; for(r=0,loop-1, for(i=0,2*loop+1, s += polcoeff(b^(3+2*r),i,y)*y^i ; ) ; ) ; ) ; } \\ _R. J. Mathar_, Apr 24 2006

%K nonn

%O 1,2

%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