A377452 - OEIS

%I #7 Oct 29 2024 09:07:06

%S 1,2,16,224,4612,126392,4340836,179534504,8693925172,482731239032,

%T 30243460133956,2110849596096584,162438922745208532,

%U 13665129603889106072,1247684652874279407076,122885960933254703151464,12987106624622962667192692,1466014441678589235669027512

%N E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x) - 1))^2.

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367161.

%F a(n) = 2 * Sum_{k=0..n} (3*k+1)!/(2*k+2)! * Stirling2(n,k).

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

%Y Cf. A052895, A377453, A377454.

%Y Cf. A367161.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 28 2024