A354340
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d + 1) )/(k * (n-k)!).
Original entry on oeis.org
1, 7, 38, 264, 1629, 16075, 122366, 1414952, 16076913, 213998983, 2112313774, 53581378400, 664573162941, 9967808211387, 239545427723062, 5933102008956848, 79857813309308609, 2677379355344673255, 44453311791217697686, 1743982053518367438616
Offset: 1
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a(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d+1))/(k*(n-k)!));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-k*x^k))))
A354851
a(n) = (n-1)! * Sum_{d|n} d^(n/d).
Original entry on oeis.org
1, 3, 8, 54, 144, 2880, 5760, 206640, 1491840, 24675840, 43545600, 10298534400, 6706022400, 1195587993600, 33476463820800, 775450900224000, 376610217984000, 553805325545472000, 128047474114560000, 339876410542276608000, 6208765924866785280000
Offset: 1
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a[n_] := (n - 1)! * DivisorSum[n, #^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)
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a(n) = (n-1)!*sumdiv(n, d, d^(n/d));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)))
A356578
Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^x.
Original entry on oeis.org
1, 0, 2, 15, 92, 1050, 8514, 147000, 1546544, 29673000, 478186920, 9011752200, 178483287432, 4205087686800, 91775320005264, 2290742704668600, 63289842765692160, 1696665419122968000, 50287699532618564544, 1549916411848463721600
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-k*x^k)^x))
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a354848(n) = (n-1)!*sumdiv(n, d, d^(n/d+1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a354848(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-3 of 3 results.