A368317 - OEIS

%I #9 Dec 21 2023 10:23:47

%S 1,5,27,161,1083,8345,74067,754241,8726283,113375465,1635899907,

%T 25961939921,449464541883,8429731963385,170261482711347,

%U 3684531041231201,85050474868523883,2085932272336772105,54168554611721580387,1484825397108091268081

%N Expansion of e.g.f. exp(4*x) / (2 - exp(x)).

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

%F a(n) = 16*A000670(n) - (3^n + 2*2^n + 4 + 8*0^n).

%o (PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));

%o a(n, m=4, t=1) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);

%Y Cf. A000670, A000629, A007047, A259533.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 21 2023