A353016 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k).
1, 1, 1, 2, 5, 11, 33, 108, 357, 1405, 5713, 24670, 117413, 574007, 3004577, 16608120, 95057925, 576245913, 3622049809, 23693870554, 161816447365, 1140392550275, 8351286979745, 63206781102116, 493344133444389, 3980464191557205, 33029872125113937, 282290255465835382
Offset: 0
Programs
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Mathematica
a[0] = 1; a[n_] := Sum[(n-2*k)^(2*k), {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 16 2022 *) -
PARI
a(n) = sum(k=0, n\2, (n-2*k)^(2*k));
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^2)))
Formula
G.f.: Sum_{k>=0} x^k / (1 - (k * x)^2).
a(n) = (A062811(n) + 1)/2 for n > 0. - Hugo Pfoertner, Apr 16 2022