A367474 - OEIS

%I #9 Nov 19 2023 08:22:23

%S 1,4,28,272,3360,50256,881616,17734944,402278496,10155145344,

%T 282329361024,8570500876032,282047266728192,10001430040080384,

%U 380152962804068352,15418451851593596928,664633482628021493760,30342827915683778027520

%N Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^2.

%F a(n) = Sum_{k=0..n} 2^k * (k+1)! * |Stirling1(n,k)|.

%F a(0) = 1; a(n) = 2*Sum_{k=1..n} (k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).

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

%Y Cf. A088500, A367475.

%Y Cf. A052801, A367470.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 19 2023