OFFSET
0,6
COMMENTS
Coefficient of q^0 is A002605.
LINKS
M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
FORMULA
Conjecture: O.g.f: 8*x^5*(1+x)*(12*x^4+24*x^3-2*x^2-16*x+5)/(2*x^2+2*x-1)^4. - R. J. Mathar, Jul 22 2009
EXAMPLE
The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=6, nu(3)=16+4q, nu(4)=44+20q+12q^2, nu(5)=120+80q+64q^2+40q^3+8q^4, so the coefficients of q^1 are 0,0,0,0,0,40.
MAPLE
nu := proc(b, lambda, n) global q; local qp, i ; if n = 0 then RETURN(1) ; elif n =1 then RETURN(b) ; fi ; qp:=0 ; for i from 0 to n-2 do qp := qp + q^i ; od ; RETURN( b*nu(b, lambda, n-1)+lambda*qp*nu(b, lambda, n-2)) ; end: A074360 := proc(n) RETURN( coeftayl(nu(2, 2, n), q=0, 3) ) ; end: for n from 0 to 30 do printf("%d, ", A074360(n)) ; od ; # R. J. Mathar, Sep 20 2006
MATHEMATICA
nu[0] = 1; nu[1] = 2; nu[n_] := nu[n] = 2*nu[n - 1] + 2*Total[q^Range[0, n - 2]]*nu[n - 2] // Expand;
a[n_] := Coefficient[nu[n], q, 3];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Nov 18 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
EXTENSIONS
More terms from R. J. Mathar, Sep 20 2006
STATUS
approved