A354843
a(n) = n! * Sum_{d|n} (n/d)^d / d!.
Original entry on oeis.org
1, 5, 19, 145, 601, 8521, 35281, 672001, 4898881, 82615681, 439084801, 21138606721, 80951270401, 3358578263041, 49506372115201, 1227603183206401, 6046686277632001, 611515751899852801, 2311256907767808001, 254421414038266675201, 4015778465971464192001
Offset: 1
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a[n_] := n! * DivisorSum[n, (n/#)^#/#! &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)
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a(n) = n!*sumdiv(n, d, (n/d)^d/d!);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, exp(k*x^k)-1)))
A354893
a(n) = n! * Sum_{d|n} d^(n - d) / (n/d)!.
Original entry on oeis.org
1, 3, 7, 73, 121, 12361, 5041, 5308801, 44452801, 5681370241, 39916801, 16800125569921, 6227020801, 35897693762810881, 2134168822456070401, 190139202281277849601, 355687428096001, 3563095308471181273190401, 121645100408832001
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(n - #)/(n/#)! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
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a(n) = n!*sumdiv(n, d, d^(n-d)/(n/d)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp((k*x)^k)-1)/k^k)))
A354844
a(n) = n! * Sum_{d|n} (n/d)^d / (d! * (n/d)!).
Original entry on oeis.org
1, 3, 4, 29, 6, 1027, 8, 26889, 272170, 861851, 12, 515592013, 14, 1530809295, 668366899216, 9382044672017, 18, 1405750464518419, 20, 1393382139935385621, 4274473667143680022, 30537988748467223, 24, 211745638285336995840025
Offset: 1
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a[n_] := n! * DivisorSum[n, (n/#)^#/(#! * (n/#)!) &]; Array[a, 25] (* Amiram Eldar, Jun 08 2022 *)
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a(n) = n!*sumdiv(n, d, (n/d)^d/(d!*(n/d)!));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k!)))
A354889
a(n) = n! * Sum_{d|n} d^(d-1) / d!.
Original entry on oeis.org
1, 4, 15, 112, 745, 10296, 122689, 2285312, 43953921, 1026157600, 25977341401, 751135431168, 23304312143281, 795924137531264, 29203006015310625, 1154107395053387776, 48661547563094964481, 2186762596692631699968, 104127471943011650364841
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(# - 1)/#! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
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a(n) = n!*sumdiv(n, d, d^(d-1)/d!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^(k-1)*x^k/(k!*(1-x^k)))))
A354898
a(n) = n! * Sum_{d|n} d^(n - d) / (d! * (n/d)!).
Original entry on oeis.org
1, 2, 2, 26, 2, 2582, 2, 268802, 7348322, 51120722, 2, 299332756802, 2, 7157951760962, 18701679546950402, 613777679843328002, 2, 3250742570192384467202, 2, 29411516073133093829529602, 1146522800008167069616128002, 4017001663590220290585602, 2
Offset: 1
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f:= proc(n) local d; n! * add(d^(n-d)/(d! * (n/d)!), d = numtheory:-divisors(n)) end proc:
map(f, [$1..30]); # Robert Israel, Jul 10 2023
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a[n_] := n! * DivisorSum[n, #^(n - #)/(#! * (n/#)!) &]; Array[a, 23] (* Amiram Eldar, Jun 11 2022 *)
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a(n) = n!*sumdiv(n, d, d^(n-d)/(d!*(n/d)!));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp((k*x)^k)-1)/(k^k*k!))))
Showing 1-5 of 5 results.