OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..296
Oleksiy Khorunzhiy, On asymptotic behavior of Bell polynomials and high moments of vertex degree of random graphs, arXiv:1904.01339 [math.PR], 2019. See (3.18). [Warning: gives wrong value 4001 for a(5).]
O. Khorunzhiy, On Asymptotic Properties of Bell Polynomials and Concentration of Vertex Degree of Large Random Graphs, Journal of Theoretical Probability (2020).
MATHEMATICA
Nest[Append[#1, 1 + #1[[-1]] + Sum[Binomial[2 #2, 2 m - 1]*#1[[#2 + 2 - m]], {m, #2}]] & @@ {#, Length@ # - 1} &, {1, 1}, 18] (* or *)
Block[{a}, a[0] = a[1] = 1; a[n_] := a[n] = 1 + a[n - 1] + Sum[Binomial[2 (n - 1), 2 m - 1] a[n - m], {m, n - 1}]; Array[a[#] &, 20, 0]] (* Michael De Vlieger, May 15 2019 *)
PROG
(PARI) a(n) = if (n<=1, 1, 1 + a(n-1) + sum(m=1, n-1, binomial(2*(n-1), 2*m-1)*a(n-m))); \\ Michel Marcus, May 15 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger and N. J. A. Sloane, May 14 2019
EXTENSIONS
More terms from Seiichi Manyama, May 15 2019
STATUS
approved