A367472 - OEIS

%I #9 Nov 19 2023 08:25:03

%S 1,6,60,816,13992,289176,6990360,193432056,6028092312,208891033656,

%T 7966989308760,331618933474296,14958464943057432,726825458489514936,

%U 37846457287387667160,2102428978611587164536,124109778776508893651352,7758254465575303379273016

%N Expansion of e.g.f. 1 / (4 - 3 * exp(x))^2.

%F a(n) = Sum_{k=0..n} 3^k * (k+1)! * Stirling2(n,k).

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

%F a(0) = 1; a(n) = 6*a(n-1) - 4*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).

%o (PARI) a(n) = sum(k=0, n, 3^k*(k+1)!*stirling(n, k, 2));

%Y Cf. A032033, A367473.

%Y Cf. A005649, A367470.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 19 2023