A377339 - OEIS

%I #20 Oct 26 2024 14:46:24

%S 1,2,4,20,144,1332,15920,225332,3758272,71711540,1544139216,

%T 37040248500,979378764320,28308318200372,887957701803952,

%U 30043664101434164,1090686549233837952,42290355849577306932,1744321111108101722768,76261355010301941319604

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377347.

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

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

%Y Cf. A377326, A377340.

%Y Cf. A377347.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 26 2024