A365012 - OEIS

%I #12 Aug 19 2023 06:29:06

%S 1,1,5,52,833,18116,498907,16648402,653034545,29450331928,

%T 1501456530131,85398143019014,5361130115439529,368227694339818132,

%U 27468201247134068891,2211469648218676671466,191131823105565504395873,17650493961604405811144624

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

%H Michael De Vlieger, <a href="/A365012/b365012.txt">Table of n, a(n) for n = 0..348</a>

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

%t Array[#!*Sum[ (2 # - k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 19, 0] (* _Michael De Vlieger_, Aug 18 2023 *)

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

%Y Cf. A052873, A365013.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 15 2023