A353013 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-k).
1, 1, 4, 28, 264, 3207, 47696, 839412, 17061280, 393264145, 10135913792, 288839201432, 9017184333440, 306045200463519, 11220008681600256, 441866073895351128, 18603606156815235584, 833860238440653331505, 39643749441387211150336
Offset: 0
Programs
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Mathematica
a[0] = 1; a[n_] := Sum[(n - 2*k)^(n - k), {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *) -
PARI
a(n) = sum(k=0, n\2, (n-2*k)^(n-k));
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k*x^2)))
Formula
G.f.: Sum_{k>=0} (k * x)^k / (1 - k * x^2).