A364942 - OEIS

%I #8 Aug 14 2023 08:28:05

%S 1,1,11,193,5037,176221,7755433,411995529,25665442841,1835264297881,

%T 148192928581581,13338664928207389,1324344628799752981,

%U 143792046846092303829,16949599953405295395521,2155710634160924802161041,294250014166281073851809457

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

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

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

%Y Cf. A361142, A364941.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 14 2023