A371826 a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-k,n-2*k).
1, 2, 8, 35, 170, 872, 4740, 26994, 161006, 1001009, 6476976, 43480373, 302250196, 2170406149, 16070240276, 122453910495, 958755921686, 7701233828576, 63381318474768, 533793776053926, 4595440308780620, 40400161269188412, 362367733795887848
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, n^k*binomial(2*n-k, n-2*k));
Formula
a(n) = [x^n] 1/((1-x-n*x^2) * (1-x)^n).
a(n) ~ exp(3*sqrt(n)/2) * n^(n/2) / 2. - Vaclav Kotesovec, Apr 07 2024