A371262 - OEIS

%I #17 Mar 17 2024 04:06:32

%S 1,0,2,3,52,365,5286,76867,1341320,27823833,624467530,16163482511,

%T 452003629452,13975370745349,467133121195118,16865722845267675,

%U 653859200911607056,27061461284541490097,1192488605596282310802,55686113074253206544167

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

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

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

%Y Cf. A371269, A371270, A371271.

%Y Cf. A371227.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 16 2024