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A308008
a(0)=a(1)=1; thereafter a(n+1) = 1 + a(n) + Sum_{m=1..n} binomial(2*n, 2*m-1)*a(n+1-m).
1
1, 1, 4, 25, 262, 3991, 82132, 2173933, 71445730, 2839498243, 133692806800, 7335280745401, 462699693768670, 33178393683900559, 2678741141802447820, 241522439552562161797, 24145570512983311489882, 2659835689591105375581595, 321076697410366882043603848, 42263134034904720594569141713
OFFSET
0,3
LINKS
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).]
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
Sequence in context: A071896 A065740 A376160 * A144281 A361589 A320569
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Seiichi Manyama, May 15 2019
STATUS
approved