A367470 - OEIS

%I #11 Nov 19 2023 08:25:11

%S 1,4,28,268,3244,47404,810988,15891628,350851564,8615761324,

%T 232911898348,6872755977388,219799913877484,7572909749244844,

%U 279630706025296108,11016315458773541548,461211305514352065004,20448268640012928321964

%N Expansion of e.g.f. 1 / (3 - 2 * exp(x))^2.

%F a(n) = Sum_{k=0..n} 2^k * (k+1)! * Stirling2(n,k).

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

%F a(0) = 1; a(n) = 4*a(n-1) - 3*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).

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

%Y Cf. A004123, A367471.

%Y Cf. A005649, A367472.

%Y Cf. A367474.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 19 2023