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A367835 Expansion of e.g.f. 1/(2 - x - exp(2*x)).

%I A367835 #16 Dec 04 2023 05:28:50
%S A367835 1,3,22,242,3544,64872,1424976,36517840,1069533824,35240047232,
%T A367835 1290137297152,51955085596416,2282489348834304,108630445541684224,
%U A367835 5567741266098944000,305752314499878569984,17909736027185859100672,1114647522476340562132992
%N A367835 Expansion of e.g.f. 1/(2 - x - exp(2*x)).
%F A367835 a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 2^k * binomial(n,k) * a(n-k).
%p A367835 A367835 := proc(n)
%p A367835     option remember ;
%p A367835     if n = 0 then
%p A367835         1 ;
%p A367835     else
%p A367835         n*procname(n-1)+add(2^k*binomial(n,k)*procname(n-k),k=1..n) ;
%p A367835     end if;
%p A367835 end proc:
%p A367835 seq(A367835(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023
%o A367835 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;
%Y A367835 Cf. A006155, A367836, A367837.
%Y A367835 Cf. A126390, A216794, A343672, A355110, A367838.
%K A367835 nonn
%O A367835 0,2
%A A367835 _Seiichi Manyama_, Dec 02 2023