A351793 - OEIS

%I #11 Feb 19 2022 10:04:17

%S 1,1,-6,6,248,-2120,-12144,458416,-2194560,-102238848,2116494080,

%T 12999644416,-1291721856000,14270887521280,650218659514368,

%U -24515781088389120,-89087389799317504,27917287109308284928,-556978307357438705664,-23150337968775391281152

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

%F a(n) = n! * Sum_{k=0..n} (-4 * (n-k))^k/k!.

%F a(0) = 1 and a(n) = n * Sum_{k=0..n-1} (-4)^(n-1-k) * binomial(n-1,k) * a(k) for n > 0.

%t a[0] = 1; a[n_] := n!*Sum[(-4*(n - k))^k/k!, {k, 0, n}]; Array[a, 20, 0] (* _Amiram Eldar_, Feb 19 2022 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(-4*x))))

%o (PARI) a(n) = n!*sum(k=0, n, (-4*(n-k))^k/k!);

%o (PARI) a(n) = if(n==0, 1, n*sum(k=0, n-1, (-4)^(n-1-k)*binomial(n-1, k)*a(k)));

%Y Column k=4 of A351791.

%Y Cf. A336952.

%K sign

%O 0,3

%A _Seiichi Manyama_, Feb 19 2022