A360989 - OEIS

%I #17 Mar 18 2023 05:00:15

%S 1,1,5,1,-231,81,55453,-40431,-30313231,33477985,29630916981,

%T -43713004191,-45378051616631,83666428734513,100216964952070541,

%U -221570666935625999,-301515678925659598623,777062158771833364929,1185517627245415533666277

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

%H Winston de Greef, <a href="/A360989/b360989.txt">Table of n, a(n) for n = 0..366</a>

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

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

%Y Cf. A141369, A196198, A360987, A360988, A360990.

%K sign

%O 0,3

%A _Seiichi Manyama_, Feb 27 2023