OFFSET
0,6
COMMENTS
Coefficient of q^0 is A006130.
LINKS
M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (4,6,-32,-19,96,54,-108,-81).
FORMULA
Conjecture: O.g.f.: 3*x^5*(3*x+1)*(36*x^4+24*x^3-29*x^2-14*x+10)/(3*x^2+x-1)^4. - R. J. Mathar, Jul 22 2009
EXAMPLE
The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=4, nu(3)=7+3q, nu(4)=19+15q+12q^2, nu(5)=40+45q+42q^2+30q^3+9q^4, so the coefficients of q^3 are 0,0,0,0,0,30.
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: A074357 := proc(n) RETURN( coeftayl(nu(1, 3, n), q=0, 3) ) ; end: for n from 0 to 30 do printf("%d, ", A074357(n)) ; od ; # R. J. Mathar, Sep 20 2006
MATHEMATICA
Join[{0, 0, 0}, LinearRecurrence[{4, 6, -32, -19, 96, 54, -108, -81}, {0, 0, 30, 168, 639, 2415, 7872, 25542}, 24]] (* Jean-François Alcover, Sep 22 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