A380639 - OEIS

%I #11 Jan 29 2025 08:10:38

%S 1,1,9,97,1297,20961,398041,8678209,213337377,5830560577,175187949481,

%T 5734893998241,203021979225649,7724154592735777,314158263983430777,

%U 13597375157683820161,623802598335834369601,30228101725367033318529,1542430410234859308052297

%N Expansion of e.g.f. exp(x/(1 - 2*x)^2).

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

%F E.g.f.: exp( Sum_{k>=1} k * 2^(k-1) * x^k ).

%F a(n) ~ 2^n * n^(n - 1/6) / (sqrt(3) * exp(n - 3*n^(2/3)/2 + 1/24)). - _Vaclav Kotesovec_, Jan 29 2025

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

%Y Cf. A380636, A380640.

%Y Cf. A082579.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Jan 28 2025