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A118934 E.g.f.: exp(x + x^4/4). 3

%I

%S 1,1,1,1,7,31,91,211,1681,12097,57961,209881,1874071,17842111,

%T 117303187,575683291,5691897121,65641390081,544238393041,

%U 3362783785777,36455473647271,485442581801311,4828464958268491,35900587138847971

%N E.g.f.: exp(x + x^4/4).

%C Equals row sums of triangle A118933.

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

%H Vincenzo Librandi, <a href="/A118934/b118934.txt">Table of n, a(n) for n = 0..200</a>

%H Marcello Artioli, Giuseppe Dattoli, Silvia Licciardi, Simonetta Pagnutti, <a href="https://arxiv.org/abs/1703.07262">Motzkin Numbers: an Operational Point of View</a>, arXiv:1703.07262 [math.CO], 2017.

%H Vaclav Kotesovec, <a href="/A118934/a118934.jpg">Graph - asymptotic (20000 terms)</a>

%F 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.

%F a(n) ~ 1/2 * n^(3*n/4) * exp(n^(1/4)-3*n/4). - _Vaclav Kotesovec_, Feb 25 2014

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

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

%Y Cf. A118933.

%K nonn

%O 0,5

%A _Paul D. Hanna_, May 06 2006

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)