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%I #11 May 10 2016 20:28:16
%S 1,1,3,7,49,321,2131,19783,195777,2101249,25721731,340358151,
%T 4902173233,75688032577,1253701725459,22347046050631,418439924732161,
%U 8318748086461953,175769214730290307,3871849719998940679,89734800330818444721,2187944831367633226561
%N Number of sets of lists (cf. A000262) whose list sizes are not a multiple of 3.
%H Alois P. Heinz, <a href="/A113775/b113775.txt">Table of n, a(n) for n = 0..445</a>
%F E.g.f.: exp(x*(1+x)/(1-x^3)).
%F a(n) = a(n-1) + 2*(n-1)*a(n-2) + 2*(n-3)*(n-2)*(n-1)*a(n-3) + 2*(n-3)*(n-2)*(n-1)*a(n-4) + (n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6). - _Vaclav Kotesovec_, Sep 25 2013
%F a(n) ~ 6^(-1/4) * n^(n-1/4) * exp(2/3*sqrt(6*n)-n) * (1 - 43/(48*sqrt(6*n))). - _Vaclav Kotesovec_, Sep 25 2013
%p nmax := 30: B := x*(1+x)/(1-x^3) : egf := 0 : for i from 0 to nmax do egf := convert(egf+taylor(B^i,x=0,nmax+1)/i!,polynom) : od: for i from 0 to nmax do printf("%d ", i!*coeftayl(egf,x=0,i)) ; od: # _R. J. Mathar_, Feb 06 2008
%p # second Maple program:
%p a:= proc(n) option remember; `if`(n=0, 1, add(`if`(0=
%p irem(j, 3), 0, a(n-j)*j!*binomial(n-1, j-1)), j=1..n))
%p end:
%p seq(a(n), n=0..25); # _Alois P. Heinz_, May 10 2016
%t CoefficientList[Series[E^(x*(1+x)/(1-x^3)), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 25 2013 *)
%Y Cf. A000726, A003724, A115276, A000246, A102736, A088009, A001590.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Jan 19 2006
%E 2 more terms from _R. J. Mathar_, Feb 06 2008
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