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%I #9 Jun 05 2016 18:20:46
%S 1,1,1,1,2,6,16,36,141,757,3361,11881,69796,541256,3364362,16217566,
%T 127028721,1288189281,10294947721,62859285817,615454153246,
%U 7709812846786,75307542579116,556618975909536,6539815832391997
%N Expansion of exp(x)/(1 - x^4/4!), where a(n) = 1 + C(n,4)*a(n-4).
%e E.g.f.: exp(x)/(1 - x^4/4!) = 1 + x + 1*x^2/2! + 1*x^3/3! + 2*x^4/4! + 6*x^5/5! + 16*x^6/6! +... + a(n)*x^n/n! +...
%e where a(n) = 1 + n*(n-1)*(n-2)*(n-3)*a(n-4)/4!.
%p G(x):=exp(x)/(1-x^4/4!): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..24); # _Zerinvary Lajos_, Apr 03 2009
%o (PARI) a(n)=n!*polcoeff(exp(x+x*O(x^n))/(1-x^4/4! +x*O(x^n)),n)
%o (PARI) /* Recurrence: */ a(n)=if(n<0,0,if(n<4,1,1 + n*(n-1)*(n-2)*(n-3)*a(n-4)/4!))
%Y Cf. A087214, A128230, A128231.
%K nonn
%O 0,5
%A _Paul D. Hanna_, Feb 20 2007
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