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!)
A118934 E.g.f.: exp(x + x^4/4). 3
1, 1, 1, 1, 7, 31, 91, 211, 1681, 12097, 57961, 209881, 1874071, 17842111, 117303187, 575683291, 5691897121, 65641390081, 544238393041, 3362783785777, 36455473647271, 485442581801311, 4828464958268491, 35900587138847971 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Equals row sums of triangle A118933.

These are the telephone numbers T^(4)_n of [Artioli et al., p. 7]. - Eric M. Schmidt, Oct 12 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Marcello Artioli, Giuseppe Dattoli, Silvia Licciardi, Simonetta Pagnutti, Motzkin Numbers: an Operational Point of View, arXiv:1703.07262 [math.CO], 2017.

Vaclav Kotesovec, Graph - asymptotic (20000 terms)

FORMULA

a(n) = a(n-1) + (n-1)*(n-2)*(n-3)*a(n-4) for n>=4, with a(0)=a(1)=a(2)=a(3)=1.

a(n) ~ 1/2 * n^(3*n/4) * exp(n^(1/4)-3*n/4). - Vaclav Kotesovec, Feb 25 2014

MATHEMATICA

With[{nn=30}, CoefficientList[Series[Exp[x+x^4/4], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jan 26 2013 *)

PROG

(PARI) a(n)=if(n<0, 0, if(n==0, 1, a(n-1) + (n-1)*(n-2)*(n-3)*a(n-4)))

CROSSREFS

Cf. A118933.

Sequence in context: A202254 A305290 A262012 * A118935 A226838 A205801

Adjacent sequences:  A118931 A118932 A118933 * A118935 A118936 A118937

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 06 2006

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 April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)