degrees of varieties K(2,n)^m / Chebyshev polynomials

Ralf Stephan ralf at
Mon May 12 14:39:18 CEST 2003

from the empiricist's gumbo:

Consider the sequences

%S A013699 1,32,610,9842,147798,2145600,30664890,435668420,6186432967
%N A013699 Degree of variety K_{2,n}^2.

That seems to be
? tc(n)=if(n==1,1,1/(1-x*tc(n-1)))
? for(n=1,30,t=polcoeff(tc(n),2*n+1):if(1,print1(t",")))
i.e., the 2n+1-th coefficient in the expansion of the n-th polynomial.

%S A013701 1,512,75025,7174454,562110290,39541748736,2610763825782,
%T A013701 165745451110910,10262482704258873
%N A013701 Degree of variety K_{2,n}^4.

And that seems to be

? for(n=1,30,t=polcoeff(tc(n),3*n+1):if(1,print1(t",")))
i.e., the 3n+1-th coefficient in the expansion of the n-th polynomial.

Please either tell me if it's known (I have no easy way to see that here)
or not, so I can either submit more terms or new sequences with the
conjecture.  Or generalize and prove it, it's all up to you.

Many thanks for your comment,

More information about the SeqFan mailing list