%I #10 Apr 10 2022 03:13:44

%S 1,0,1,2,19,393,15177,939394,85063260,10599342278,1739073390797,

%T 363404567436467,94224446795779884,29683590039199285223,

%U 11167286542016941966714,4945143125245884296040780,2546112368234517215955646341,1508197687055444623135714912377

%N a(n) = Sum_{k=0..floor(n/2)} (n-k)^(n-2*k) * |Stirling1(n-k,k)|.

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

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

%o (PARI) a(n) = sum(k=0, n\2, (n-k)^(n-2*k)*abs(stirling(n-k, k, 1)));

%Y Cf. A343579, A353255, A353256.

%Y Cf. A353289.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Apr 09 2022