A367835 - OEIS

%I #16 Dec 04 2023 05:28:50

%S 1,3,22,242,3544,64872,1424976,36517840,1069533824,35240047232,

%T 1290137297152,51955085596416,2282489348834304,108630445541684224,

%U 5567741266098944000,305752314499878569984,17909736027185859100672,1114647522476340562132992

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

%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 2^k * binomial(n,k) * a(n-k).

%p A367835 := proc(n)

%p     option remember ;

%p     if n = 0 then

%p         1 ;

%p     else

%p         n*procname(n-1)+add(2^k*binomial(n,k)*procname(n-k),k=1..n) ;

%p     end if;

%p end proc:

%p seq(A367835(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023

%o (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 Cf. A006155, A367836, A367837.

%Y Cf. A126390, A216794, A343672, A355110, A367838.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 02 2023