OFFSET
0,2
LINKS
Christian Gaetz and Yibo Gao, Separable elements in Weyl groups, arXiv:1905.09331 [math.CO], 2019.
FORMULA
G.f.: (3 - 4*x - 5*x^2 - (1 - x)*sqrt(1 - 6*x + x^2))/(1 - x + sqrt(1 - 6*x + x^2)).
D-finite with recurrence +2*(n+1)*a(n) +3*(-5*n+3)*a(n-1) +(18*n-43)*a(n-2) +3*(3*n-14)*a(n-3) +2*(-n+6)*a(n-4)=0. - R. J. Mathar, Mar 25 2024
MATHEMATICA
b[0] = 1 ; a[0] = 1; a[1] = 2; a[2] = 4;
b[n_Integer] :=
b[n] = b[n - 1] + Sum[b[k]*b[n - 1 - k], {k, 0, n - 1}];
a[n_Integer] :=
a[n] = a[n - 1] + b[n - 2] + 2*b[n - 1] +
Sum[b[k]*a[n - k - 1], {k, 0, n - 3}]; Table[a[n], {n, 0, 30}] (* Andy Huchala, Aug 01 2023 *)
PROG
(Sage)
prec = 10
R.<x> = PowerSeriesRing(QQ, prec)
f = (3 - 4*x - 5*x^2 - (1 - x)*sqrt(1 - 6*x + x^2))/(1 - x + sqrt(1 - 6*x + x^2))
list(f) # Andy Huchala, Jul 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Fern Gossow, Jul 30 2023
STATUS
approved