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%I #10 Aug 29 2020 02:13:31
%S 1,1,3,12,67,461,3823,36933,407963,5068909,69982083,1062784273,
%T 17607354955,316012688213,6108011298847,126490611884013,
%U 2794122884322635,65578524701197341,1629676370022564219,42748628870263418761,1180373377691425730235
%N E.g.f.: 1 / (2 + x^3/6 - exp(x)).
%H Robert Israel, <a href="/A337059/b337059.txt">Table of n, a(n) for n = 0..426</a>
%F a(0) = a(1) = 1; a(n) = n * (a(n-1) + (n-1) * a(n-2) / 2) + Sum_{k=4..n} binomial(n,k) * a(n-k).
%p S:= series(1/(2+x^3/6-exp(x)),x,31):
%p seq(coeff(S,x,i)*i!,i=0..30); # _Robert Israel_, Aug 28 2020
%t nmax = 20; CoefficientList[Series[1/(2 + x^3/6 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = a[1] = 1; a[n_] := a[n] = n (a[n - 1] + (n - 1) a[n - 2]/2) + Sum[Binomial[n, k] a[n - k], {k, 4, n}]; Table[a[n], {n, 0, 20}]
%Y Cf. A000670, A032032, A124504, A232475, A337058.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 13 2020
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