A367836 - OEIS

%I #12 Feb 16 2024 13:47:46

%S 1,4,41,627,12759,324543,9906453,352785933,14358074211,657405969075,

%T 33444798498657,1871613674744553,114259520317835871,

%U 7556674046930376111,538212358684663414317,41071433946325564954581,3343141735414440335583003

%N Expansion of e.g.f. 1/(2 - x - exp(3*x)).

%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 3^k * binomial(n,k) * a(n-k).

%t With[{nn=20},CoefficientList[Series[1/(2-x-Exp[3x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 16 2024 *)

%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, 3^j*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A006155, A367835, A367837.

%Y Cf. A284859, A343673, A355111.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 02 2023