A360756 Expansion of Sum_{k>0} (x * (1 + 2 * x^k))^k.
1, 3, 1, 5, 1, 11, 1, 9, 13, 11, 1, 45, 1, 15, 41, 49, 1, 79, 1, 117, 85, 23, 1, 297, 81, 27, 145, 309, 1, 483, 1, 481, 221, 35, 561, 1165, 1, 39, 313, 2121, 1, 1143, 1, 1365, 2437, 47, 1, 4081, 449, 3411, 545, 2341, 1, 4699, 5281, 4889, 685, 59, 1, 20445, 1, 63, 6217
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, 2^(n/# - 1) * Binomial[#, n/# - 1] &]; Array[a, 60] (* Amiram Eldar, Aug 02 2023 *)
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PARI
my(N=70, x='x+O('x^N)); Vec(sum(k=1, N, (x*(1+2*x^k))^k)) -
PARI
a(n) = sumdiv(n, d, 2^(n/d-1)*binomial(d, n/d-1));
Formula
a(n) = Sum_{d|n} 2^(n/d-1) * binomial(d,n/d-1).
If p is an odd prime, a(p) = 1.