A360712
Expansion of Sum_{k>0} (k * x * (1 + k*x^k))^k.
Original entry on oeis.org
1, 5, 27, 272, 3125, 46915, 823543, 16781312, 387421218, 10000078125, 285311670611, 8916102153177, 302875106592253, 11112006865911623, 437893890381640625, 18446744074783358976, 827240261886336764177, 39346408075327943829273
Offset: 1
-
a[n_] := DivisorSum[n, #^(#+n/#-1) * Binomial[#, n/# - 1] &]; Array[a, 20] (* Amiram Eldar, Aug 09 2023 *)
-
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x*(1+k*x^k))^k))
-
a(n) = sumdiv(n, d, d^(d+n/d-1)*binomial(d, n/d-1));
A359442
a(n) = Sum_{d|n} d^(n + 1 - d - n/d).
Original entry on oeis.org
1, 2, 2, 4, 2, 15, 2, 74, 83, 643, 2, 12635, 2, 117715, 397188, 2359426, 2, 103572204, 2, 1260918355, 13841818644, 25937425627, 2, 5612318393211, 152587890627, 23298085126579, 1853020231898564, 2422197090649523, 2, 1032944452284531101, 2, 10376297939508166658
Offset: 1
-
a[n_] := DivisorSum[n, #^(n + 1 - # - n/#) &]; Array[a, 32] (* Amiram Eldar, Aug 09 2023 *)
-
a(n) = sumdiv(n, d, d^(n+1-d-n/d));
-
my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k/k)))
A359730
a(n) = Sum_{d|n} 2^(d-1) * d^(n/d).
Original entry on oeis.org
1, 5, 13, 41, 81, 245, 449, 1185, 2413, 5585, 11265, 26693, 53249, 118081, 248733, 535041, 1114113, 2390885, 4980737, 10557201, 22050797, 46265345, 96468993, 201795717, 419480401, 873123841, 1812204685, 3760019521, 7784628225, 16111126325, 33285996545, 68729044993
Offset: 1
-
a[n_] := DivisorSum[n, 2^(#-1) * #^(n/#) &]; Array[a, 32] (* Amiram Eldar, Aug 14 2023 *)
-
a(n) = sumdiv(n, d, 2^(d-1)*d^(n/d));
-
my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k*2^(k-1)*x^k/(1-k*x^k)))
Showing 1-3 of 3 results.