A356530
Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k^k).
Original entry on oeis.org
1, 1, 4, 18, 156, 1020, 23040, 189000, 8462160, 174741840, 8418513600, 110288455200, 26670240273600, 364684824504000, 46300470369753600, 5169242034644688000, 359472799348030368000, 7508907247291081632000, 6157317530690533823616000
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)^(1/k^k))))
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a356529(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=1, i, a356529(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356486
a(n) = (n-1)! * Sum_{d|n} d^n / (d-1)!.
Original entry on oeis.org
1, 5, 29, 358, 3149, 98196, 824263, 73122736, 784270089, 158028202000, 285315299411, 855386690484096, 302875585593853, 5876921233326141376, 111916280261483009775, 73985874496557113890816, 827240282809126652177, 1625215094103508198780449024
Offset: 1
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a[n_] := (n-1)! * DivisorSum[n, #^n / (#-1)! &]; Array[a, 18] (* Amiram Eldar, Aug 30 2023 *)
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a(n) = (n-1)!*sumdiv(n, d, d^n/(d-1)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-(k*x)^k)/k!)))
A356524
Expansion of e.g.f. Product_{k>0} 1/(1 - k * x^k)^(1/k!).
Original entry on oeis.org
1, 1, 4, 15, 100, 565, 5946, 46039, 605256, 6646329, 103614490, 1320840631, 27185208876, 401901829069, 9042437722878, 168984439301175, 4257225193170256, 85582303577644465, 2593970612953642386, 57441717948059605927, 1862688382990615542900
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k*x^k)^(1/k!))))
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a354849(n) = (n-1)!*sumdiv(n, d, d^(n/d)/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354849(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-3 of 3 results.