A361828 - OEIS

%I #14 Mar 26 2023 10:25:24

%S 1,1,2,7,40,338,3841,54821,939335,18744832,426390069,10881017916,

%T 307686450208,9546443638409,322375619648549,11769010007246745,

%U 461834905502223078,19384809864763869231,866564718107731746860,41102477939620052536314

%N a(0) = 1; a(n+1) = Sum_{k=0..n} k^k * a(n-k).

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

%F a(n) ~ exp(-1) * n^(n-1). - _Vaclav Kotesovec_, Mar 26 2023

%t nmax = 20; CoefficientList[Series[1/(1 - x - x*Sum[(k*x)^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 26 2023 *)

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

%Y Cf. A000312, A051295, A277610.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Mar 26 2023