A358741 - OEIS

%I #12 Feb 18 2023 03:26:54

%S 1,1,9,179,6655,400581,35530421,4357960999,706230728379,

%T 146116931998025,37577989723572001,11758017370126904091,

%U 4398121660346674034039,1938019214715102033590029,993580299268226843514372045,586357970017371399763899232271

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

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

%F a(n) ~ n! * n^n. - _Vaclav Kotesovec_, Feb 18 2023

%t nmax = 20; CoefficientList[1 + Series[Sum[k! * (k * x/(1 - x))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 18 2023 *)

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

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

%Y Cf. A358738, A358740.

%Y Cf. A355494.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 29 2022