A353015 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^n.
1, 1, 4, 27, 257, 3157, 47385, 839928, 17168097, 397517868, 10283523826, 293950435376, 9200707298514, 312972062711525, 11496160809184370, 453507273286873875, 19122193920118268355, 858239308206920523297, 40851073484808464297979
Offset: 0
Programs
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Mathematica
a[0] = 1; a[n_] := Sum[(n-3*k)^n, {k, 0, Floor[n/3]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 16 2022 *) -
PARI
a(n) = sum(k=0, n\3, (n-3*k)^n);
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-(k*x)^3)))
Formula
G.f.: Sum_{k>=0} (k * x)^k / (1 - (k * x)^3).