A356540
Expansion of e.g.f. Product_{k>0} 1/(1 - (3 * x)^k)^(1/3^k).
Original entry on oeis.org
1, 1, 6, 40, 496, 5400, 114400, 1760080, 47671680, 1090230400, 34312096000, 916877068800, 39605683532800, 1211405062067200, 55580939301888000, 2260295506653184000, 115398744818925568000, 4928605977341190144000, 305987190350116667392000
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(3*x)^k)^(1/3^k))))
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a356539(n) = sumdiv(n, d, d*3^(n-d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a356539(j)*v[i-j+1]/(i-j)!)); v;
A356529
a(n) = (n-1)! * Sum_{d|n} d^(n-d+1).
Original entry on oeis.org
1, 3, 8, 78, 144, 14400, 5760, 5851440, 88583040, 5859786240, 43545600, 24077414592000, 6706022400, 35948640894566400, 4395744249613516800, 263312496059348736000, 376610217984000, 5901087844517892009984000, 128047474114560000
Offset: 1
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a[n_] := (n - 1)! * DivisorSum[n, #^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Aug 10 2022 *)
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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^k)))
A356538
Expansion of e.g.f. Product_{k>0} 1/(1 - (2 * x)^k)^(1/2^k).
Original entry on oeis.org
1, 1, 5, 27, 249, 2085, 30645, 354375, 6542865, 108554985, 2330525925, 45331607475, 1288779532425, 28889867731725, 876160258298325, 25315531795929375, 860642393272286625, 26527678331237708625, 1063065483349950205125, 36393649136002135852875
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(2*x)^k)^(1/2^k))))
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a090879(n) = sumdiv(n, d, d*2^(n-d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a090879(j)*v[i-j+1]/(i-j)!)); v;
A356560
Expansion of e.g.f. Product_{k>0} 1/(1 - k^2 * x^k)^(1/k^2).
Original entry on oeis.org
1, 1, 4, 18, 156, 1020, 16560, 143640, 2898000, 43016400, 926856000, 13749674400, 524416939200, 8626888670400, 284030505158400, 7950850859952000, 284397434953632000, 6752059834744224000, 357295791069689472000, 9098085523917918528000
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k^2*x^k)^(1/k^2))))
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a308688(n) = sumdiv(n, d, d^(2*n/d-1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a308688(j)*v[i-j+1]/(i-j)!)); v;
A356561
Expansion of e.g.f. Product_{k>0} 1/(1 - k^3 * x^k)^(1/k^3).
Original entry on oeis.org
1, 1, 4, 18, 204, 1260, 37440, 299880, 11002320, 204860880, 6618628800, 92924647200, 8181137764800, 124123075876800, 7211104918617600, 288085376346768000, 14964000305173920000, 340302035937191328000, 42619767305209750656000
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k^3*x^k)^(1/k^3))))
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a308689(n) = sumdiv(n, d, d^(3*n/d-2));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a308689(j)*v[i-j+1]/(i-j)!)); v;
Showing 1-5 of 5 results.