A356436
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d) )/k.
Original entry on oeis.org
1, 5, 23, 146, 874, 8124, 62628, 707664, 7860816, 103284000, 1179669600, 24454569600, 324615427200, 5740203974400, 119579523436800, 2688723275212800, 46084905896601600, 1383333631684300800, 26411386476116275200, 868104140064602112000
Offset: 1
-
a(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d))/k);
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)/(1-x)))
A356440
Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^(1/(1-x)).
Original entry on oeis.org
1, 1, 8, 99, 2444, 101450, 7045194, 701736966, 97147459184, 17505366041880, 4005462950166600, 1128394974054308400, 384386423684496873672, 155497732356686080354968, 73718160600338917089657216, 40462026280443230503858113240
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(k*x)^k)^(1/k))^(1/(1-x))))
-
a356437(n) = n!*sum(k=1, n, sigma(k, k)/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356437(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356588
Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^x.
Original entry on oeis.org
1, 0, 2, 9, 44, 450, 2754, 45360, 340304, 6481944, 81801000, 1370631240, 21731534472, 511117017840, 8113055559504, 193958323289640, 4765385232157440, 108183734293844160, 2754467397591689664, 80416694712647352960, 2132862160676063137920, 67803682111729108433280
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k*x^k)^(1/k))^x))
-
a055225(n) = sumdiv(n, d, d^(n/d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*a055225(j-1)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-3 of 3 results.
