A354890
a(n) = n! * Sum_{d|n} d^n / d!.
Original entry on oeis.org
1, 6, 33, 472, 3245, 157896, 828583, 132078976, 1578211209, 307174074400, 285351587411, 1835340563252736, 302881333613053, 11743240652094910336, 336123967242674523375, 149825956013958069846016, 827240617573764860177, 3551697093896307129060647424
Offset: 1
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a[n_] := n! * DivisorSum[n, #^n/#! &]; Array[a, 18] (* Amiram Eldar, Jun 10 2022 *)
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a(n) = n!*sumdiv(n, d, d^n/d!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!*(1-(k*x)^k)))))
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)))
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!))))
A358593
a(n) = n! * Sum_{d|n} d^(n-d) / d!^(n/d).
Original entry on oeis.org
1, 3, 7, 49, 121, 2701, 5041, 219521, 1587601, 33446701, 39916801, 17731796545, 6227020801, 2879710009177, 98069239768501, 2418218838097921, 355687428096001, 2832293713653708877, 121645100408832001, 2295597943489176040001, 71029619657111138063041
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(n-#) / #!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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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, x^k/(k!-(k*x)^k))))
A357296
Expansion of e.g.f. Sum_{k>0} x^k / (k! * (1 - x^k/k)).
Original entry on oeis.org
1, 3, 7, 31, 121, 851, 5041, 43261, 369601, 3748249, 39916801, 490801081, 6227020801, 87861842641, 1310800947457, 21018206008801, 355687428096001, 6419518510204801, 121645100408832001, 2435836129700029057, 51102829650622464001, 1124549558817839481601
Offset: 1
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a[n_] := n! * DivisorSum[n, 1/(#^(n/#-1) * #!) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!*(1-x^k/k)))))
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a(n) = n!*sumdiv(n, d, 1/(d^(n/d-1)*d!));
Showing 1-5 of 5 results.