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)))))
A354891
a(n) = n! * Sum_{d|n} d^(n - d) / d!.
Original entry on oeis.org
1, 3, 7, 73, 121, 9721, 5041, 1760641, 44452801, 562615201, 39916801, 3156125575681, 6227020801, 192873372531841, 222245415808416001, 14806216643368550401, 355687428096001, 34884164976924636172801, 121645100408832001
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(n - #)/#! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
-
a(n) = n!*sumdiv(n, d, d^(n-d)/d!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!*(1-(k*x)^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
-
a[n_] := n! * DivisorSum[n, #^(# - 1)/#! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
-
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)))))
A354899
a(n) = n! * Sum_{d|n} d^d / (d! * (n/d)!).
Original entry on oeis.org
1, 5, 28, 281, 3126, 48517, 823544, 16995617, 387692650, 10047310481, 285311670612, 8932562801857, 302875106592254, 11119129387084097, 437899615088648176, 18451106376806703617, 827240261886336764178, 39349894934527426209025
Offset: 1
-
a[n_] := n! * DivisorSum[n, #^#/(#! * (n/#)!) &]; Array[a, 18] (* Amiram Eldar, Jun 11 2022 *)
-
a(n) = n!*sumdiv(n, d, d^d/(d!*(n/d)!));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1)/k!)))
A354900
a(n) = n! * Sum_{d|n} d^d / (n/d)!.
Original entry on oeis.org
1, 9, 163, 6193, 375001, 33602521, 4150656721, 676462516801, 140587148681281, 36288005670120961, 11388728893445164801, 4270826391670469473921, 1886009588552176549862401, 968725766890781857146309121, 572622616354852243874626732801
Offset: 1
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a[n_] := n! * DivisorSum[n, #^#/(n/#)! &]; Array[a, 15] (* Amiram Eldar, Jun 11 2022 *)
-
a(n) = n!*sumdiv(n, d, d^d/(n/d)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1))))
Showing 1-5 of 5 results.