A367853 - OEIS

%I #7 Dec 03 2023 01:44:08

%S 1,2,12,128,1952,38464,926336,26323968,861419520,31882358784,

%T 1316275003392,59954841649152,2985997926727680,161401148097036288,

%U 9408988894966579200,588381964243109412864,39285329204482179858432,2789234068575581984784384

%N Expansion of e.g.f. 1/(1 - x + log(1 - 4*x)/4).

%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 4^(k-1) * (k-1)! * binomial(n,k) * a(n-k).

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

%Y Cf. A052820, A367851, A367852.

%Y Cf. A352071, A355112, A367847.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 02 2023