A007167 Number of skeins with 2n+1 edges. (Formerly M3504)

1, 1, 4, 15, 62, 271, 1247, 5938, 29113, 145815, 743384, 3844314, 20118681, 106348391, 567002169, 3045455865, 16463622763, 89509216860, 489103356753, 2684663659765, 14795752770278, 81841297482116, 454202999050433, 2528381760697852

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..23.

R. C. Read, On the enumeration of a class of plane multigraphs, Aequat. Math. 31 (1986) no 1, 47-63.

Prog

(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

Crossrefs

Sequence in context: A275871 A007161 A352815 * A036728 A027216 A124541

Adjacent sequences: A007164 A007165 A007166 * A007168 A007169 A007170

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from R. J. Mathar, Apr 24 2006

More terms from Sean A. Irvine, Nov 07 2017

Status

approved