A367181 - OEIS

%I #15 Nov 10 2023 09:35:10

%S 1,1,3,22,261,4186,85035,2096242,60793257,2028053146,76512294567,

%T 3221179205410,149713378082301,7614267616582810,420634056602820099,

%U 25081994054279063506,1605673188973569254481,109838361160586478627226,7995918540574019507985471

%N E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x)^2.

%H Seiichi Manyama, <a href="/A367181/b367181.txt">Table of n, a(n) for n = 0..362</a>

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

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

%Y Cf. A000272, A367180.

%Y Cf. A365546, A367179.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 08 2023