OFFSET
1,4
LINKS
Erwan Brugallé and Grigory Mikhalkin, Enumeration of curves via floor diagrams, C. R. Acad. Sci. Paris, Ser. I, 345 (2007), 329-334; arXiv:0706.0083 [math.AG], 2007.
Penka Georgieva and Aleksey Zinger, Enumeration of real curves in CP^{2n-1} and a Witten-Dijkgraaf-Verlinde-Verlinde relation for real Gromov-Witten invariants, Duke Math. J., 166 (2017), 3291-3347; arXiv:1309.4079 [math.SG], 2013-2017. See Eq. (7.1).
FORMULA
a(n) ~ c * d^n * n^(2*n-3), where d = 0.22437689379499207235291475487670864472074175469311760751181993..., c = 2.114876309952735589169436238081913983666848627651832555153... - Vaclav Kotesovec, Apr 28 2024
MATHEMATICA
n[1] = nt[1] = 1;
n[d_] := n[d] = Sum[With[{d2 = d - d1}, (d2^2 Binomial[2 d - 3, 2 d1 - 2] - d1 d2 Binomial[2 d - 3, 2 d1 - 1]) nt[d1] n[d2]], {d1, d - 1}];
nt[d_] := nt[d] = d n[d] + Sum[With[{d2 = d - d1}, (d1 d2^2 Binomial[2 d - 2, 2 d1 - 1] - d2^3 Binomial[2 d - 2, 2 d1 - 2]) nt[d1] n[d2]], {d1, d - 1}];
Table[n[d], {d, 20}] (* Andrey Zabolotskiy, May 03 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 27 2010
EXTENSIONS
Name edited, terms a(8) and beyond added by Andrey Zabolotskiy, May 03 2022
STATUS
approved