login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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).]

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: A210809 A071896 A065740 * A144281 A320569 A058791

Adjacent sequences:  A308005 A308006 A308007 * A308009 A308010 A308011

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)