%I #10 Feb 26 2023 08:42:33

%S 1,1,1,10,159,8306,1346855,801620870,2064941077199,20691706495244482,

%T 1137052204448926181679,255128692791512749880418782,

%U 348784909594653094321340422905383,2262992285674206001784964011734257207938

%N Expansion of e.g.f. Sum_{k>=0} exp((k^k - 1)*x) * x^k/k!.

%F G.f.: Sum_{k>=0} x^k/(1 - (k^k - 1)*x)^(k+1).

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+x+sum(k=2, N, exp((k^k-1)*x)*x^k/k!)))

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k^k-1)*x)^(k+1)))

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

%Y Cf. A001831, A360933, A360934.

%Y Cf. A355464.

%K nonn,easy

%O 0,4

%A _Seiichi Manyama_, Feb 26 2023