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a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-k,n-2*k).
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%I #9 Apr 07 2024 17:43:57

%S 1,2,8,35,170,872,4740,26994,161006,1001009,6476976,43480373,

%T 302250196,2170406149,16070240276,122453910495,958755921686,

%U 7701233828576,63381318474768,533793776053926,4595440308780620,40400161269188412,362367733795887848

%N a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-k,n-2*k).

%F a(n) = [x^n] 1/((1-x-n*x^2) * (1-x)^n).

%F a(n) ~ exp(3*sqrt(n)/2) * n^(n/2) / 2. - _Vaclav Kotesovec_, Apr 07 2024

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

%Y Cf. A371825, A371827.

%Y Cf. A171180.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 07 2024